Read GA.Geom.STPW.ppi-iv text version

Georgia Standardized Test Practice Workbook

McDougal Littell

correlated to the

GEORGIA QUALITY CORE CURRICULUM

and the

GEORGIA HIGH SCHOOL GRADUATION TEST STANDARDS

Geometry

Applying · Reasoning · Measuring

Georgia Geometry Standardized Test Practice Workbook

The Standardized Test Practice Workbook provides practice exercises for every lesson in a standardized test format. Included are multiple-choice, quantitativecomparison, and multi-step problems. The Standardized Test Practice for every lesson is correlated to the Georgia Quality Core Curriculum and to the Georgia High School Graduation Test standards. At the end of the book you will find practice for the Georgia End-of-Course Test.

Copyright © 2001 McDougal Littell Inc. All rights reserved. Permission is hereby granted to teachers to reprint or photocopy in classroom quantities the pages or sheets in this work that carry a McDougal Littell copyright notice. These pages are designed to be reproduced by teachers for use in their classes with accompanying McDougal Littell material, provided each copy made shows the copyright notice. Such copies may not be sold, and further distribution is expressly prohibited. Except as authorized above, prior written permission must be obtained from McDougal Littell Inc. to reproduce or transmit this work or portions thereof in any other form or by any other electronic or mechanical means, including any information storage or retrieval system, unless expressly permitted by federal copyright law. Address inquiries to Manager, Rights and Permissions, McDougal Littell Inc., P. O. Box 1667, Evanston, Illinois 60204.

ISBN: 0-618-13259-7 123456789-MDI- 04 03 02 01 00

Contents

Chapter Title

1 2 3 4 5 6 7 8 9 10 11 12 Basics of Geometry Reasoning and Proof Perpendicular and Parallel Lines Congruent Triangles Properties of Triangles Quadrilaterals Cumulative Standardized Test Practice Transformations Similarity Right Triangles and Trigonometry Circles Area of Polygons and Circles Surface Area and Volume Georgia End-of-Course Practice Test Answers 1­7 8­13 14­20 21­27 28­33 34­40 41­44 45­50 51­57 58­64 65­71 72­77 78­84 85­88 A1-A8

Copyright © McDougal Littell Inc. All rights reserved.

Geometry

Georgia Standardized Test Practice Workbook

iii

LESSON

1.1

GA QCC: 4, 6

Standardized Test Practice

For use with pages 3­9

TEST TAKING STRATEGY

Read each test question carefully. Always look for shortcuts that will allow you to work through a problem more quickly.

5. Multiple Choice

1. Multiple Choice

Choose the next figure in

Choose the next figure in

the pattern.

the pattern.

Chapter 1

A

B

C

A

B

C

D D E

E

2. Multiple Choice

What is the next number in

6. Multiple Choice

the sequence? 2,

A D

The first three objects in a pattern are shown. How many blocks are in the next object?

1, 9

4, 11

7. . .

B E

10 12

C

10

3. Multiple Choice

What is the next number in

A D

the sequence? 0, 2, 6, 12 . . .

A D

20 36

B E

25 40

C

30

18 22

B E

24 26

C

20

7. Multi-Step Problem

Examine the triangular

pattern. 1 1 1 2 1

4. Multiple Choice

What is the next number in

the sequence? 2, 4, 16 . . .

A D

28 256

B E

26 192

C

12

1 1 3 3 1 a. Predict the next two rows of the triangle.

b. Describe a pattern for the value of a num-

ber in each row.

c. Describe a pattern for the number of

entries in each row.

Copyright © McDougal Littell Inc. All rights reserved.

Geometry

Georgia Standardized Test Practice Workbook

1

LESSON

1.2

GA QCC: 7, 9, 12

Standardized Test Practice

For use with pages 10­16

TEST TAKING STRATEGY

Work as quickly as you can through the easier sections but avoid making careless errors on easy questions.

7. Multiple Choice

1. Multiple Choice

What does the symbol BC

B D

AB and BD intersect at

B E

represent?

A

? line BC ray BC

A D

. A D B

C

segment BC point B ray CB

C

Chapter 1

C E

none of these

8. Multiple Choice

Multiple Choice In Exercises 2­6, refer to the diagram below.

b M X Y Q R P N O Z c d a

Points W, X, Y and Z are not coplanar. What is the intersection of plane WXY and WYZ? A WX B WY C W and Y

D E

The planes do not intersect. Cannot be determined.

9. Multi-Step Problem

Follow the directions below to sketch the desired shape.

a. Draw a plane. Label the four corners A, B, 2. Name a point that is collinear to points N

and Z.

A D

P P and X

B E

O O and M

C

M

3. Name a point that lies on line c. A D

C, and D, starting at the bottom left and proceeding clockwise. b. Draw four parallel lines, AE, BF, CG, and DH, so that each line intersects plane ABCD once, and points E, F, G, and H are coplanar. Plane ABCD and plane EFGH are parallel.

c. Draw EH, HG, FG, and EF. d. What shape is outlined by the figure?

M Q

B E

P O

C

Z

4. Name a point that is collinear to points P

and Q.

A D

M X

B E

N M and Y

C

Y

5. Name a point that is coplanar to line a. A D

N Q

B E

O all of these

C

R

6. Name three noncollinear points. A D

P, Y, Q Q, R, O

B E

M, N, P X, N, P

C

M, N, Z

2

Geometry

Georgia Standardized Test Practice Workbook

Copyright © McDougal Littell Inc. All rights reserved.

LESSON

1.3

GA QCC: 7, 8, 9, 12, 43, 46

Standardized Test Practice

For use with pages 17­25

GHSGT: 9, 19, 20, 35

TEST TAKING STRATEGY

Sketch graphs or figures in your test booklet to help you solve the problems. Even though you must keep your answer sheet neat, you can make any kind of mark you want in your test booklet.

8. Multiple Choice

1. Multiple Choice A C E

A rule that is accepted without proof is called a ? . theorem axiom B and C

B D

postulate A and B

Point H is between G and I. Use the segment addition postulate to solve for x when GH 8x 7, HI 3x 2, and GI 38. 3 31

B E

Chapter 1

A D

5 39

C

7

2. Multiple Choice A D

Find the length of AC if AB is 6, BC is 10, and B is between A and C. 4 60

B E

9. Multiple Choice

In Exercise 8, the length

B E

of HI is

A D

?

. 5 39

C

16 6

C

4

3 31

7

Multiple Choice In Exercises 3­7, use the diagram below where MQ 30, MN 5, MN NO and OP PQ.

M N O P Q

10. Multiple Choice

Use points A 5, 1 , B 5, 6 , C 1, 4 and D 4, 2 to determine which of the following is true. AB AB BC BC BD CD

B D

A C C

AB AC

CD AB

3. Find the length of OQ. A D

5 20

B E

10 25

15

E

Quantitative Comparison

4. Find the length of PQ. A D

In Exercises 11­13, choose the statement below that is true about the given values.

A B C

5 20

B E

10 25

C

15

The value in column A is greater. The value in column B is greater. The two values are equal. The relationship cannot be determined from the information given. Column A Column B XY when X 5, 2 and Y 1, 4 XY when X 5, 3 and Y 8, 2 XY YZ

5. Find the length of NO. A D

5 20

B E

10 25

C

15

D

6. Find the length of NP. A D

11. C

5 20

B E

10 25

15

12. 13.

AB when A 1, 3 and B 3, 6 AB when A 2, and B 3, 2 XZ 4

7. Which of the statements below are not true? A C E

NP NQ MQ

MN MP PQ

PQ B

D

MP MO

OQ PQ

Geometry

Georgia Standardized Test Practice Workbook

3

3

Copyright © McDougal Littell Inc. All rights reserved.

LESSON

1.4

GA QCC: 8, 9

Standardized Test Practice

For use with pages 26­32

GHSGT: 29, 31

TEST TAKING STRATEGY

Avoid spending too much time on one question. Skip questions that are too difficult for you, and spend no more than a few minutes on each question.

6. Multiple Choice

1. Multiple Choice A

Angle A is an obtuse angle for which measure(s)? 0 < m A < 90 0 < m A < 180 90 < m A < 180 m A m A 90 180 An angle measuring 35 ? .

B D

Plot the points A 6, 4 , B 1, 1 and C 3, 1 in a coordinate plane. Sketch ABC. The angle is a(n) ? . acute angle right angle adjacent angle

B D

Chapter 1

B C D E

A C E

obtuse angle straight angle

7. Multiple Choice

2. Multiple Choice

would be a(n)

A C E

Using the same three points in Exercise 6, sketch ACB. The angle is a(n) ? . acute angle right angle adjacent angle

B D

acute angle right angle adjacent angle

obtuse angle straight angle

A C E

obtuse angle straight angle

3. Multiple Choice

Which angle appears to be

B

a right angle?

A

8.

Quantitative Comparison

following information.

Use the 50 90 m EBF

C

D

· D is interior to ABE · m ABD · E is interior to DBF · m EBC · F is interior to EBC · m ABD

Choose the statement below that is true about the given values.

E 4. Multiple Choice A C E A

The value in column A is greater. The value in column B is greater. The two values are equal. The relationship cannot be determined from the information given. Column A m ABC Column B m ABE m EBC

Find m WYZ.

B D

B C

5 85 175

90 105

W X

45 40

D

Y

Z

5. Multiple Choice

Find the measure of

m BDC.

A B C D E

4

185 115 25 175 100

Geometry

B A

35 150

D

C

Georgia Standardized Test Practice Workbook

Copyright © McDougal Littell Inc. All rights reserved.

LESSON

1.5

GA QCC: 9, 15, 43, 46

Standardized Test Practice

For use with pages 34­42

GHSGT: 4, 31

TEST TAKING STRATEGY

Staying physically relaxed during the SAT is very important. If you find yourself tensing up, put your pencil down and take a couple of deep breaths. This will help you stay calm.

6. Multiple Choice

1. Multiple Choice

5 2, 5 2, 3 2 1 2

Find the midpoint of a segment with endpoints A 3, 2 and B 8, 1 .

B E

11 1 2,2 11 2, 3 2

m DBC

A D

BD bisects ABC. If the 28 , what is the m ABD?

B E

A D

C

11 2,

1 2

14 62

28 152 QS bisects 52 13

M

52

C

56

Chapter 1

2. Multiple Choice A C E

Find the midpoint of a segment with endpoints A 7, 3 and B 3, 3 . 2, 5, 0 5, 3 3

B D

7. Multiple Choice

MQR. What

is the m MQR?

A C E

2, 0 2, 0

26 104 38

B D

S

Q

R

3. Multiple Choice

Find the coordinates of the other endpoint of a segment with an endpoint of X 13, 5 and midpoint M 8, 3 . 18, 7 3, 7 29, 11

B D

8. Multiple Choice

AB bisects 56 28

C

CAD. Find

the value of x.

A C E

A C E

18, 1 3, 1

2 5 6

B D

(8x

20)

B

(x

1 2

25

)

A

4. Multiple Choice

Find the coordinates of the other endpoint of a segment with an endpoint of X 2, 3 and midpoint M 1, 2 . 4, 0, 4, 8 7 1

B D

D

Quantitative Comparison

A C E

4, 7 5, 8

In Exercises 9 and 10, use the diagram below where BD bisects ABC and BE bisects ABD. Choose the statement below that is true E A about the given values. 28

A B C D

D

5. Multiple Choice A B C D E

Choose the congruent angles on the triangle shown. A and A and and B C C

A C B

The value in column A is greater. The value in column B is greater.

B

C

The two values are equal. The relationship cannot be determined. Column A Column B m DBC 180

AB and AC AB and BC

9. 10.

m ABE

m EBD

m ABD

Copyright © McDougal Littell Inc. All rights reserved.

Geometry

Georgia Standardized Test Practice Workbook

5

LESSON

1.6

GA QCC: 8, 9, 12

Standardized Test Practice

For use with pages 44­50

GHSGT: 29, 31

TEST TAKING STRATEGY

The mathematical portion of the SAT is based on material taught in your high school mathematics courses. One of the best ways to prepare for the SAT is to keep up with your regular studies and do your homework assignments.

6. Multiple Choice

(3x 2)

Multiple Choice Refer to the diagram below for Exercises 1­3.

Chapter 1

Find the value of x.

(4x 5)

2 3 1 5 4

A D

13.3 26

B E

7 25

C

14

7. Multiple Choice 1. Which angles are a linear pair? A C E

1 and 1 and 3 and

2 4 5

B D

2 and 4 and

3 5

Two angles are complementary. One angle has a measure that is twice the other angle. What is the measure of the smaller angle? 15 60

B E

A D

30 75

C

45

2. Which angles are vertical angles? A C E

8. Multiple Choice

Find the value of y.

(2x 8)

1 and 3 and 4 and

2 5 5

B D

1 and 1 and

5 4

(4x 12) (7y 12)

A 3. Which angles are supplementary? A C E D

10 152

B E

28 128

C

20

1 and 1 and

4 5

B D

4 and B and C

5

Quantitative Comparison

all of these

In Exercises 9 and 10, use the diagram below and choose the statement below that is true about the given value. The m 3 76 .

A B C D

4. Multiple Choice

Two angles are supplementary. One angle has a measure that is five less than four times the other. What is the measure of the larger angle? 19 148

B E

The value in column A is greater. The value in column B is greater. The two values are equal.

1

2 4 3

A D

71 153

C

143

5. Multiple Choice A C E

What is the m 1? 90 145

35 1

The relationship cannot be determined from the given information. Column A m 3 Column B m 1 The supplement of 1

45 55 155

B D

9. 10.

m 4

6

Geometry

Georgia Standardized Test Practice Workbook

Copyright © McDougal Littell Inc. All rights reserved.

LESSON

1.7

GA QCC: 12, 37, 46

Standardized Test Practice

For use with pages 51­58

GHSGT: 4, 9, 21, 26, 27, 35

TEST TAKING STRATEGY

Make sure you are familiar with the directions before taking a standardized test. This way, you do not need to worry about the directions during the test.

7. Multiple Choice

1. Multiple Choice

Find the perimeter of the 8 16

3 5

Find the area of the figure.

y

figure.

A C E

A 18.84 square units B D B C

7 14 30

9.42 square units

Chapter 1

28.26 square units

1 1 x

D 56.52 square units

2. Multiple Choice

the circle. Use

A B C D E

Find the circumference of 3.14.

E

88.74 square units

18.84 ft 37.68 ft 113.04 ft 37.68 ft2 113.04 ft2

8. Multiple Choice

6 ft

Find the area of the rectangle defined by A 2, 1 , B 2, 4 , C 6, 4 and D 6, 1 . 7 square units 24 square units 9 square units

B D

A C E

14 square units 12 square units

3. Multiple Choice A D

Find the area of a square with a side of 7 inches. 14 in. 49 in.2

B E

9. Multiple Choice A D

28

in.2

C

49 in.

A square with an area of 64 square inches has a perimeter of ? . 64 in. 128 in.

B E

28 in.

16 in.

C

32 in.

4. Multiple Choice A D

Find the area of a triangle with a base of 8 m and a height of 4 m. 19 m 16 m

B E

cannot be determined

10. Multiple Choice

32 12

m2 m2

C

16

m2

A triangle has an area of 72 square feet and a height of 9 feet. Find its base. 16 ft 9 ft

B E

A 5. Multiple Choice A C E

8 ft 34 ft

C

32 ft

Find the area of a circle with a radius of 9 meters. Use 3.14. 28.26 m2 56.52 m2 254.34 m2 Find the area of the figure.

B D

D

28.26 m 56.52 m

11. Multi-Step Problem

A rectangular window pane is 40 inches by 50 inches.

a. Find the area of the window pane. b. Find the perimeter of the window pane.

6. Multiple Choice A B C D E

c. A frame around the window pane is

50.24 25.12

cm2 cm2

16 cm

401.92 cm2 200.96 cm2 100.48 cm2

1.5 inches wide. Find the area and perimeter of the window pane, including the frame. With the frame, by what percent did the area increase?

Copyright © McDougal Littell Inc. All rights reserved.

Geometry

Georgia Standardized Test Practice Workbook

7

LESSON

2.1

GA QCC: 5, 6, 9

Standardized Test Practice

For use with pages 71­78

TEST TAKING STRATEGY

When checking your work, try to use a method other than the one you originally used to get your answer. If you use the same method, you may make the same mistake twice.

D E

1. Multiple Choice A B C D E

What is the if-then form of "A group is a dozen if it has 12 objects?" If a group does not have 12 objects, then it is not a dozen. If a group is not a dozen, then it does not have 12 objects. If a group has 12 objects, then it is a dozen. A group is a dozen if and only if it has 12 objects. None of the above

If 5x

2

13, then x

3.

None of the above

5. Multiple Choice A B C D E

Which of the following statements is not true? If x If x3 If x If x If x2 4, then x2 27, then x 3, then 2, then x2 4, then x x3 4. 2. 16. 3. 27.

2. Multiple Choice

Chapter 2

What is the inverse of "If water is ice, then the water's temperature is 32 F?" If water's temperature is 32 F, then it is ice. If water is not ice, then its temperature is not 32 F. If water's temperature is not 32 F, then water is not ice. Water is ice if and only if its temperature is 32 F. None of the above

6. Multiple Choice

A B C D E

Use the conditional statement "If an angle is obtuse, then the angle measures 98 " to decide which of the following are true.

I. The statement is true. II. The converse of the statement is true. III. The contrapositive of the statement is true. A I only B II only

C E

III only I and III

D

I and II

3. Multiple Choice A B C D E

What is the converse of "If you are hungry, then you did not eat lunch?" If you did not eat lunch, then you are hungry. If you ate lunch, then you are not hungry. If you are not hungry, then you ate lunch. You are hungry if and only if you did not eat lunch. None of the above What is the contrapositive 3, then 5x 2 13?" 13 if and only if x 2 13. 3. 2 13, then x 3. 3, then 5x

7. Multi-Step Problem

Use Postulate 8 to

answer parts (a)­(e). Postulate 8: Through any three noncollinear points there exists exactly one plane.

a. Rewrite Postulate 8 in if-then form. b. Write the converse of Postulate 8. c. Write the inverse of Postulate 8. d. Write the contrapositive of Postulate 8. e. Critical Thinking

4. Multiple Choice

of "If x

A B C

8

5x If x If 5x

2

Are the statements you wrote in parts (a)­(d) true?

Geometry

Georgia Standardized Test Practice Workbook

Copyright © McDougal Littell Inc. All rights reserved.

LESSON

2.2

GA QCC: 4, 6, 8

Standardized Test Practice

For use with pages 79­85

TEST TAKING STRATEGY

If you find yourself spending too much time on one test question and getting frustrated, move to the next question. You can revisit a difficult problem later with a fresh perspective.

4. Multiple Choice

1. Multiple Choice

Given that 2 4 and 2 5, which statement about the diagram is not true? 5 4 6 and 2 are supplementary. 8 and 5 are supplementary. 1 1 and 8 3 are supplementary.

A B C D E

Which of the following is true about the conditional statement "If m 1 30 and the m 2 150 , then the angles are supplementary?"

1 2 5 6

3 4 7 8

I. The statement is true. II. The converse is true. III. The statement can be written as a true biconditional.

A D

I I and II

B E

II I, II, and III

C

III

2. Multiple Choice

What is the biconditional form of the statement "If a whitetail deer has antlers, then it is a male deer?" A whitetail deer has no antlers if and only if it is not a male deer. A whitetail deer has antlers if and only if it is a male deer. If a whitetail deer has no antlers, then it is not a male deer. If a whitetail deer is male, then it has antlers. None of the above

5. Multiple Choice A B C D E

Which statement below would be a true biconditional statement? If ABC measures 90 , then it is a right angle. If two angles are adjacent, then they share a common side. If two squares have the same diagonal length, then they have equal sides. A and C All of the above

Chapter 2

A B C D E

Quantitative Comparison

3. Multiple Choice

Which one of the following statements cannot be written as a true biconditional statement? If the sum of two angles is 90 , then they are complementary. If two angles have the same measurement, then they are congruent. If 5x 7 22, then x 3. If two angles are linear, then they are supplementary. If y lies between x and z, then xy yz xz.

In Exercises 6 and 7, choose the statement below that is true about the given quantities.

A B C D

The quantity in column A is greater. The quantity in column B is greater. The two quantities are equal. The relationship cannot be determined from the given information. Column A Column B

The number of lines that can be drawn through any one point The sum of two adjacent angles

A B C D E

6.

The number of lines created by the intersection of two planes The sum of two supplementary angles

7.

Copyright © McDougal Littell Inc. All rights reserved.

Geometry

Georgia Standardized Test Practice Workbook

9

LESSON

2.3

GA QCC: 4, 5, 6

Standardized Test Practice

For use with pages 87­95

GHSGT: 4

TEST TAKING STRATEGY

It is important to remember that your SAT score will not solely determine your acceptance into a college or university. Do not put added pressure on yourself to do well. If you are not satisfied with your SAT score, remember you can take it again.

5. Multiple Choice

Multiple Choice For Exercises 1­3, let p be "It is raining," let q be "It is thundering," and let r be "We cannot swim."

1. What is q p? A B C D E

Which law of logic allows the conclusion given the true statement? "If it is Saturday, then Nina's family rents movies. Today is Saturday, therefore Nina concludes her family will rent movies." Law of Detachment Law of Syllogism Inductive reasoning Deductive reasoning None of the above

If it is raining, then it is thundering. If it is raining, then we cannot swim. If it is thundering, then it is raining. If it is thundering, then we cannot swim. If it is not raining, then it is not thundering.

A B C D E

Chapter 2

2. What is the converse of p q? A B C D E

6. Multiple Choice

If it is thundering, then it is raining. If it is not raining, then it is not thundering. If it is not thundering, then it is not raining. If it is not thundering, then it is raining. If it is thundering, then it is not raining.

Which law of logic allows the conclusion given the true statement? "For the past 4 weeks the ski club has gone skiing on Friday nights. Wendy concludes that the ski club will go skiing this Friday." Law of Detachment Law of Syllogism Inductive reasoning Deductive reasoning None of the above

A B C D

3. What is the contrapositive of r q? A B C D E

E

If it is thundering, then we cannot swim. If we can swim, then it is not thundering. If we cannot swim, then it is not thundering. If we can swim, then it is thundering. If it is not thundering, then we can swim. The statement ~p ~r

7. Multi-Step Problem

Let p be "You get caught exceeding the speed limit," let q be "You will get a speeding ticket," and let r be "You will pay higher insurance rates."

a. Write p q in words. b. Write q r in words. c. Write the contrapositive of p q in

4. Multiple Choice

could be

A B C D E

10

?

.

the inverse of r p the inverse of ~r ~p the contrapositive of r p the converse of r p the contrapositive of ~r ~p

Geometry

Georgia Standardized Test Practice Workbook

words and symbols.

d. Writing

Use the Law of Syllogism and the statements from parts (a) and (b) to write a new conditional statement. How does the Law of Detachment apply?

Copyright © McDougal Littell Inc. All rights reserved.

LESSON

2.4

GA QCC: 1, 2, 6, 43

Standardized Test Practice

For use with pages 96­101

GHSGT: 3, 4, 38

TEST TAKING STRATEGY

Do not panic if you run out of time before answering all of the questions. You can still receive a high test score without answering every question.

5. Multiple Choice

1. Multiple Choice

Which property of equality matches the conditional statement "If AB BC and BC CD, then AB CD?" Addition property Symmetric property Reflexive property Substitution property Transitive property

Which property of equality matches the conditional statement "If XY AB 15 and XY 5, then AB 10?" Substitution property Addition property Division property Distributive property Reflexive property

A B C D E

A B C D E

2. Multiple Choice

Which property of equality matches the conditional statement "If m X m Z, then m Z m X?" Addition property Symmetric property Reflexive property Substitution property Transitive property

6. Multiple Choice

Use the Multiplication property of equality to complete "If m A 15 , then 4 m A ? . 15 60

B E

A B C D E

A D

30 75

C

45

Chapter 2

7. Multi-Step Problem

m ABE m DBC.

In the diagram, m EBC and m EBD

State a reason that makes each statement true.

3. Multiple Choice

Solve 5x 10, then choose the property that applies to the required step. Substitution property Addition property Division property Distributive property Reflexive property

A E

A B C D E

D B C

a. m EBC b. m ABE c. m ABE d. m EBD e. m ABE f. m ABE g. Writing

m EBD m EBC m EBD m DBC m EBD 2 m EBD

m DBC m DBC m EBD

4. Multiple Choice

Solve x 7 10, then choose the property that applies to the required step. Substitution property Addition property Division property Distributive property Reflexive property

A B C D E

Use parts (a)­(f) to write an argument for "If m ABE m EBC and m EBD m DBC, then m ABE 2 m EBD ."

Copyright © McDougal Littell Inc. All rights reserved.

Geometry

Georgia Standardized Test Practice Workbook

11

LESSON

2.5

GA QCC: 4, 6, 9

Standardized Test Practice

For use with pages 102-107

GHSGT: 5

TEST TAKING STRATEGY

Make sure that you are familiar with the directions before taking a standardized test. This way, you do not need to worry about the directions during the test.

YZ.

5. Multiple Choice

W Z

7x 14 3x 2

1. Multiple Choice

5x 1 9x

In the diagram, WX Find the length of XZ.

3 11

In WXYZ, WZ What is the value of x?

X

XY.

W

X

Y

A D

11 4

B E

2 26

C

15

Z Y

2. Multiple Choice

and BC

3x 2

In the diagram, AB CD. Find the length of CE.

6y 7

DE

A D

1.6 12

B E

3 4

C

0.25

y C

8

11x

6

Quantitative Comparison

10

A

B

D

E

Chapter 2

A D

11 16

B E

22 5

C

In Exercises 6­8, use the diagram below to choose the statement that is true about the given value.

A B C D

The value in column A is greater. The value in column B is greater. The two values are equal. The relationship cannot be determined from the given information.

X Y

5

3. Multiple Choice

In KLM, KL LM, and KL 8, and KM 8. Give a reason why KL and KM are congruent. Reflexive property Symmetric property Definition of congruent segments Transitive property Addition property

L

A B C D E

Z

5

K

M W V

4. Multiple Choice

In the figure from Exercise 3, KL LM and LM KM. Give a reason that KL KM. Reflexive property Transitive property Symmetric property Definition of congruent segments Addition property

6. 7. 8.

Given: Y is the midpoint of XZ, XW ZV, and XZ WV. Column A WY WV WV ZV Column B YV 3 ZV 2 XY 2 YZ

A B C D E

12

Geometry

Georgia Standardized Test Practice Workbook

Copyright © McDougal Littell Inc. All rights reserved.

LESSON

2.6

GA QCC: 6, 8, 9

Standardized Test Practice

For use with pages 109­116

GHSGT: 4

TEST TAKING STRATEGY

Staying physically relaxed during the SAT is very important. If you find yourself tensing up, put your pencil down and take a couple of deep breaths. This will help you stay calm.

6. Multiple Choice A B C D E

1. Multiple Choice

complementary. If

A D

Two angles 1 and 2 are 1 is 27 , what is 2? 54 153

C

Solve for y in the diagram.

(3x 18)

20 45 51 78 102

(5x

27 63

B E

90

2)

2(y

6)

2. Multiple Choice

Two angles, 1 and 2, are supplementary to 3. If m 1 85 , then m 1 m 3 ? . 85 265

B E

A D

170 180

C

90

7. Multiple Choice

3. Multiple Choice

What is m 2 if

Given that 1 is not a right angle, 1 and 2 form a linear pair, 3 and 4 form a linear pair, and 1 and 3 are vertical angles. Which statement below is not true? m 1 m 3 2 m 2 1 m 4 m 4 4 m 4 3 180 180 180

Chapter 2

m 1

35 .

A B

2

1

C

A D

35 145

B E

70 55

C

90

D E

Quantitative Comparison

4. Multiple Choice

If m 3 64 128

126 , then

m 2

A C E

?

B D

.

63 126 36

In Exercises 8­10, choose the statement that is true about the diagram. In the diagram, 4 5, m 3 40 , m 6 120 , and m 3 m 5 m 9 180 .

A

1 2 4 3

B 5. Multiple Choice A C E

Solve for x in the diagram. 4 16

(3x 2) (13x 18)

2 8 1

B D

C D

The value in column A is 1 2 11 3 4 greater. The value in column B is 10 9 5 6 7 8 greater. The two values are equal. The relationship cannot be determined from the given information. Column A Column B 4m 7 m 11 m 10

Geometry 13

8. 9. 10.

Copyright © McDougal Littell Inc. All rights reserved.

m 1 m 9 2m 4

Georgia Standardized Test Practice Workbook

LESSON

3.1

GA QCC: 8, 9, 11, 12

Standardized Test Practice

For use with pages 129­134

GHSGT: 29

TEST TAKING STRATEGY

1. Multiple Choice

Work as quickly as you can through the easier sections, but avoid making careless errors on easy questions. Multiple Choice

In Exercises 6­8, use the diagram below. Think of each segment as part of a line.

I G a C E A B D F J H

In the diagram, how many lines can be drawn through point X that are skew to line a? 0 2

B D

A C E

1 3

X

More than 3

Multiple Choice

diagram below.

In Exercises 2­5, use the

a

6. AC and HF are A

b c

?

B D

. skew intersecting

1 2 3 4 5 6 7 8

perpendicular parallel None of these DH and CD and JH GH

C E

7. Which lines are skew to BF? 2. Which angles are corresponding angles? A C E A C E B D

CA and IG

1 and 2 and A and C

5 6

B D

4 and A and B

6

A and B

B and C CD and HF and CA CA GH and EF

8. Which lines are perpendicular to CG? A C E B D

3. Which angles are alternate exterior angles?

Chapter 3

A C E

2 and 3 and A and C

8 8

B D

2 and A and B

7

A and B

B and C

9. Multi-Step Problem

4. Which angles are consecutive interior angles? A C E

Use the diagram below to answer parts (a)­(d). Think of each segment as part of a line.

E A F D G C H

3 and 3 and A and C

5 7

B D

4 and A and B

6

5. What type of angles are A B C D E

14

4 and

5?

B

Corresponding angles Alternate exterior angles Alternate interior angles Consecutive interior angles Consecutive exterior angles

Geometry

Georgia Standardized Test Practice Workbook

a. Name all lines parallel to AD. b. Name all lines skew to FG. d. Critical Thinking

c. Name all lines perpendicular to BF.

If you did not know ABC was a right angle, which answers above would be affected?

Copyright © McDougal Littell Inc. All rights reserved.

LESSON

3.2

GA QCC: 6, 9, 12

Standardized Test Practice

For use with pages 136­141

GHSGT: 29

TEST TAKING STRATEGY

Avoid spending too much time on one question. Skip questions that are too difficult for you, and spend no more than a few minutes on each question.

5. Multiple Choice

1. Multiple Choice A C E

Find the value of x. 35 145

55

Find the value of y from

B E

55 90 125

B D

Exercise 4.

A

x

35 110

70 90

C

55

D

2. Multiple Choice A C E

Find the value of x. 50 65

x b

2 3 1 25

Quantitative Comparison

25 90 155

B D

For Exercises 6­8, use the diagram below. Choose the statement that is true about the given values. Given: x

A

y 35

y

m 5

3. Multiple Choice

Which of the following must be true if a b? I. 1 and 2 are complementary. m 2 < 180 m 2

B D

B

a

C D

II. m 1 III. m 1

A C E

2 The value in 1 3 column A is x 4 6 5 greater. The value in column B is greater. The values are equal. The relationship cannot be determined from the given information.

Column A II only I and III

7. 8. 6.

Column B m 6 m 3 m 6

Chapter 3

I only I and II I, II, and III

m 2 m 1

m 4 m 2

m 3

m 5

4. Multiple Choice A B C D E

Find the value of x.

35 70 55 110 90

35

y x

Copyright © McDougal Littell Inc. All rights reserved.

Geometry

Georgia Standardized Test Practice Workbook

15

LESSON

3.3

GA QCC: 1, 9, 11, 12, 15

Standardized Test Practice

For use with pages 143­149

GHSGT: 4, 29

TEST TAKING STRATEGY

Sketch graphs or figures in your test booklet to help you solve the problem. Even though you must keep your answer sheet neat, you can make any kind of mark you want in your test booklet.

5. Multiple Choice

1 2 3 4 5 6 7 8

Multiple Choice

For Exercises 1­4, use the diagram at the right, where a b.

1. Choose the reason

Which of the following is not true when a b? 1 4 m 2 m 1 180 m 4 180 m 4 5 and 8 m 6 m 5

7 5 8 3 6 1 4 2

a

A B C D E

a

b

the statement "If the m 1 85 , then m 5 85 " is true.

A B C D E

b

m 6 m 8

Alternate Interior Angles Theorem Alternate Exterior Angles Theorem Consecutive Interior Angles Theorem Vertical Angles Theorem Corresponding Angles Postulate

Quantitative Comparison

In Exercises 6­8, use the diagram below where a b and x y. Choose the statement that is true about the given values.

x

125 1 4 5 8 9 12 13 2 6 7 3

2. Choose the reason the statement "If the

y a

m 3

A B C

55 , then m 5

135 " is true.

Alternate Interior Angles Theorem Alternate Exterior Angles Theorem Consecutive Interior Angles Theorem Vertical Angles Theorem Corresponding Angles Postulate

A B C D

10 11 14 15

b

Chapter 3

D E

3. Choose the reason the statement "If the

m 2

A B C D E

110 , then m 7

70 " is true.

Alternate Interior Angles Theorem Alternate Exterior Angles Theorem Consecutive Interior Angles Theorem Vertical Angles Theorem Corresponding Angles Postulate 120 , then the m 3

B E 6. 7.

The value in column A is greater. The value in column B is greater. The two values are equal. The relationship cannot be determined from the given information. Column A m 2 m 10 m 6 Column B m 8 m 3 m 12

4. If the m 6 A D

?

C

.

8.

m 4

m 14

60 90

120

180

cannot be determined

16

Geometry

Georgia Standardized Test Practice Workbook

Copyright © McDougal Littell Inc. All rights reserved.

LESSON

3.4

GA QCC: 6, 9, 11, 12

Standardized Test Practice

For use with pages 150­156

GHSGT: 29

TEST TAKING STRATEGY

When checking your work, try to use a method other than the one you originally used to get your answer. If you use the same method, you may make the same mistake twice.

t x

1. Multiple Choice

4. Multiple Choice A B

y

Which postulate or theorem would prove x y?

A

What value of x would make lines w and v parallel? 30 20 60 40 50 EB AE EF FD CF BC

(3x 60) 120

w

Consecutive Interior Angles Converse Corresponding Angles Converse Alternate Interior Angles Converse Alternate Exterior Angles Converse

C D E

v

B C D E

5. Multiple Choice A B

Which lines are parallel?

E

70 30 30

Cannot prove x y with given information

F

68 32

2. Multiple Choice

C D

t

Which postulate or theorem would prove a b?

A

A

B C

D

B and C All of the above

E

Consecutive Interior Angles Converse

6. Quantitative Comparison

a b

Use the diagram below to find the values of x and y that would make a b.

B C D E

Corresponding Angles Converse Alternate Interior Angles Converse Alternate Exterior Angles Converse Cannot prove a b with given information

t

142 28 (4y (2x 25) 15) (x 30)

a

Chapter 3

3. Multiple Choice

b

Which postulate or theorem would prove x y?

A

x y

Choose the statement that is true about the given values.

A B C D

Consecutive Interior Angles Converse Corresponding Angles Converse Alternate Interior Angles Converse Alternate Exterior Angles Converse

B C D E

The value in column A is greater. The value in column B is greater. The two values are equal. The relationship cannot be determined from the given information. Column A x Column B y

Cannot prove x y with given information

Copyright © McDougal Littell Inc. All rights reserved.

Geometry

Georgia Standardized Test Practice Workbook

17

LESSON

3.5

GA QCC: 1, 9, 12, 15

Standardized Test Practice

For use with pages 157­164

GHSGT: 4, 29

TEST TAKING STRATEGY

It is important to remember that your SAT score will not solely determine your acceptance into a college or university. Do not put added pressure on yourself to do well. If you are not satisfied with your SAT score, remember that you can take it again.

4. Multiple Choice

1. Multiple Choice

Complete the following to make a true statement. "In a plane, if two lines are to the same line, then they ? are to each other." ? perpendicular, parallel perpendicular, perpendicular parallel, parallel parallel, perpendicular None of these

J

30 30

Which of the statements must be true if a b and x y? m 1 m 5

a

1 2 3 6 7 4 5 8 9

I.

b x y

A B C D E

II. m 3 m 5 180 III. m 7 m 8 180

A C

I only III only All of the above

B D

II only I and II

2. Multiple Choice

Which theorem or postulate shows J K?

A B C D E

E

K t

5. Multiple Choice

Determine which lines

a b c d e

Alt. Int. Converse Cons. Int. Alt. Ext. Cons. Ext. Corresp. Converse Converse Converse Postulate

t

must be parallel.

A B C D E

a b c d c e A and B A and C

Chapter 3

3. Multiple Choice

Which theorem or postulate shows J K?

A B C D E

6. Multiple Choice

J K

What value of x makes

a b

(2x 30)

a b?

A B C D

Alt. Int. Converse Cons. Int. Converse Alt. Ext. Cons. Ext. Corresp. Converse Converse Postulate

10 30 50 70 90

x

T

E

7. Multi-Step Problem

Given a b, m n, and

m n

2 3 4

m. a. Prove a

b. Prove b

a

n. n.

1 5 6

a b

18

Geometry

Georgia Standardized Test Practice Workbook

Copyright © McDougal Littell Inc. All rights reserved.

LESSON

3.6

GA QCC: 12, 44

Standardized Test Practice

For use with pages 165­171

GHSGT: 29, 43

TEST TAKING STRATEGY

Read each test question carefully. Always look for shortcuts that will allow you to work through a problem more quickly.

6. Multiple Choice

y

1. Multiple Choice A D

Find the slope of the line that passes through 5, 2 and 8, 1 . 1

1 3

Which lines are parallel?

B E

1 2

C

1 3

( 2, 7) ( 3, 5)

(0, 6)

2. Multiple Choice

Which equation of the line has a slope of 5 and passes through point 2, 1 ? y y y 5x 5x 11x 11 9 5

B D

(0, 3) ( 3, 2)

1

c

(0, 0)

2

x

A C E

y y

5x 5x

2 11

A D

a

b

a b None

B E

b c All 3

C

a c

3. Multiple Choice

Which equation of the line has a y-intercept of 6 and is parallel to 1 y 2? 2x y y y

1 2x 1 2x

7. Multiple Choice

A C E

6 6 6

B D

y y

1 2x 1 2x

6 6

A line k has equation 2 x 1. If k i and i passes through y 3 point 4, 1 , what is the equation of i? y y y

2 3x 2 3x 2 3x 11 3

A C E

B D

y y

2 3x

3 2x 11 3

4

2x

4 1

4. Multiple Choice

Which equation of the line passes through 3, 2 and is parallel to y 2x? 3

A C E

Quantitative Comparison

y y y

2 3x 2 3x 2 3x

2 4 4

B D

y y

2 3x 2 3x

In Exercises 8 and 9, choose the statement below which is true about the given values.

A B C D

Chapter 3

3

5. Multiple Choice A C E

Which of the following is an equation of a line parallel to 4y 8 3x? y y y

3 4x 3 4x 4 3x

The value in column A is greater. The value in column B is greater. The two values are equal. The relationship cannot be determined from the given information. Column A Column B The slope of the line passing through 7, 3 and 11, 2 The y-intercept of the line passing through 1, 2 and 4, 1

6 1

B D

y y

4 3x

2 4

8.

3x

The slope of the line passing through 7, 5 and 4, 6 The y-intercept of 3 y 4x

9.

Copyright © McDougal Littell Inc. All rights reserved.

Geometry

Georgia Standardized Test Practice Workbook

19

LESSON

3.7

GA QCC: 2, 9, 11, 12, 44, 46

Standardized Test Practice

For use with pages 172­178

GHSGT: 43

TEST TAKING STRATEGY

Do not panic if you run out of time before answering all of the questions. You can still receive a high test score without answering every question.

6. Multiple Choice

1. Multiple Choice A D

Which is the slope of a line perpendicular to the line y 2x 6? 2 6

B E

1 2 1 6

Which lines are perpenB

dicular?

A

C

1 2

y y y y

1 2x 1 2x 2 3x 3 2x

6 1 3 1

y y y y

3x 5x 2x 1 2x

1 3

3 3 2

2. Multiple Choice A C E

Which equation of a line is 2 1 perpendicular to y 5x 3? y y y

5 2x 2 5x 5 2x

C

D

3 3 6

B D

y y

5 2x

2 3

E

None of these

3x

7. Multiple Choice w: y n: y p: y z: y

3 2x 2 3x 3 2x 2 3x

Which of the following statements are true about lines w, n, p, and z?

2 6 3 1

3. Multiple Choice

The product of the slopes of two nonvertical perpendicular lines is ? . 0 2

B E

A D

1

C

1 I. w

A C E

Cannot be determined with given information

p

II. n z

III. z

B D

p

I only III only II and III

II only I and II

4. Multiple Choice

A line k has equation 8 x 3. If k l and l passes through y 11 point 4, 3 , what is the equation of line l? y y y

1 2 x. 11 8x 8 11 x 11 8x 5 2 5 2 17 2

A

B D

y y

Chapter 3

C E

8 1 11 x 11 11 17 8x 2

8. Multi-Step Problem a. On a coordinate plane, plot points A 2, 1

and B 5, 2 .

b. Find the equation of the line x passing

5. Multiple Choice

A line i has equation If i j and j passes through point y 6, 2 , what is the equation of j? y y y 2x 2x

1 2x

through points A and B.

c. Find the equation of the line y, perpendicu-

A C E

14 10 10

B D

y y

2x 2x

14 10

lar to line x and passing through point A.

d. Find the equation of the line z, parallel to

line y and passing through point B.

e. Critical Thinking

If the bottom of a rectangle lies along line x, and its sides lie on lines y and z, find the slope of the line representing the top.

20

Geometry

Georgia Standardized Test Practice Workbook

Copyright © McDougal Littell Inc. All rights reserved.

LESSON

4.1

GA QCC: 10, 13

Standardized Test Practice

For use with pages 194­201

GHSGT: 22, 29, 31

TEST TAKING STRATEGY

If you find yourself spending too much time on one test question and getting frustrated, move on to the next question. You can revisit a difficult problem later with a fresh perspective.

6. Multiple Choice

1. Multiple Choice A B C D E

A triangle with three acute angles and no congruent sides is ? . an equiangular triangle a right triangle an isosceles triangle an obtuse triangle an acute scalene triangle .

Find the measure of

D C

(3x 10)

BCD.

A B C D E

50 120 60 160 20

40

A

B

(2x

20)

2. Multiple Choice A B C D E

A triangle with side lengths of 5 cm, 3 cm, and 5 cm is ? an equilateral triangle an obtuse triangle an isosceles triangle an acute triangle a scalene triangle

7. Multiple Choice A B C D E

Find the measure of

1.

40 40 70 80 1 140 Cannot be determined Find the measure of 1.

1 60 65

3. Multiple Choice

classified as

A B C D E

The triangle below can be ? .

95

8. Multiple Choice A B C D E 9.

acute isosceles acute scalene obtuse isosceles obtuse scalene right scalene ?

50 90 60 30 85

Quantitative Comparison

4. Multiple Choice

classified as

A B C D E

The triangle below can be .

Choose the statement below which is true about the given number. The value in column A is greater. The value in column B is greater. The two values are equal. The relationship cannot be determined from the given information.

4

acute isosceles acute scalene obtuse isosceles obtuse scalene right scalene

35 35

A B C D

Chapter 4

5. Multiple Choice

An isosceles triangle has a perimeter of 82 cm. The lengths of the legs of the triangle are represented by 3x 2 and 5x 14 . Find the length of the base of the triangle. 8 cm 30 cm

B E

3 125 1 30 2

Column A m 1

Column B m 2

Geometry 21

A D

16 cm 52 cm

C

26 cm

Copyright © McDougal Littell Inc. All rights reserved.

Georgia Standardized Test Practice Workbook

LESSON

4.2

GA QCC: 10, 14, 16

Standardized Test Practice

For use with pages 202­210

TEST TAKING STRATEGY

1. Multiple Choice A C E

One of the best ways to prepare for the SAT is to keep up with your regular studies and do your homework.

6. Multiple Choice

XYZ, which If ABC of the following statements below is not true? B CBA BAC Y YXZ

B

K

Given M C, find the value of x.

K B

B and

AB AC

XY XZ

40

ZXY D

2x

(3x

5)

2. Multiple Choice

F

In the diagram, EFG HIJ. What is the measure of H?

I

65 35

M

L A C

A D

43 58

B E

40 29

C

82

Quantitative Comparison

G J H

E

A D

35 80 ? .

B E

65

C

70

In Exercises 7 and 8, use the given information to find the indicated value. Choose the statement below that is true about the given value. The value in column A is greater. The value in column B is greater. The two values are equal. The relationship cannot be determined from the given information. Given: ABCD EFGH

A B C D

C B A 2x

100 50

Cannot be determined

3. Multiple Choice

In the diagram in Exercise

B E

2, EG

A D

HI FG Z

HJ

C

JI

Cannot be determined N and

4. Multiple Choice

Given X O, find the value of x.

N

E

8y F 18

D

32

Y

20 75

H Z M

(5x 10)

G

X

Column A

7.

Column B y m GHE

O

x m CBD

A D

19 85

B E

38 20

C

95

8.

Chapter 4

5. Multiple Choice A D

Use the diagram in Exercise 4 to find m Z. 19 85

B E

38 20

C

95

22

Geometry

Georgia Standardized Test Practice Workbook

Copyright © McDougal Littell Inc. All rights reserved.

LESSON

4.3

GA QCC: 6, 14, 15, 16

Standardized Test Practice

For use with pages 212­219

GHSGT: 4, 22

TEST TAKING STRATEGY

1. Multiple Choice

Work as quickly as you can through the easier sections, but avoid making careless errors on easy questions.

Statements

a.

Use the diagram below. Which additional congruence is correct to prove ABC DEF?

D B

Reasons

a. 3.

AE

CD CDE CDE

b. AED c. ED ED d. AED

b. 4. c. 5. d. 6.

A

Statements

C F E

Reasons

e. 7. f. 8. g. 9.

e. B is the midpoint

A B C D E

B E by SAS Congruence Postulate BC FE by SSS Congruence Postulate A D by SAS Congruence Postulate A or B B or C

of AD and EC. BC BE, AB BD g. ABE DBC

f. 10. Multiple Choice

2. Multiple Choice

Use the diagram below. Which congruence is correct to prove XYZ JKL?

X J

In rectangle ABCD, a diagonal is drawn from B to D. Which statement is not true? DAB AB BC CBD In ADB BCD

B D

A C E

ABD DB DB

CDB

11. Multiple Choice

Z Y K L

MNO and XYZ, MN XY and NO YZ. If the triangles are congruent, what else must be true? N MO Y XZ

B D

A B C D E

Y K by SAS Congruence Postulate XY JK by SAS Congruence Postulate ZY LK by SAS Congruence Postulate A or B B or C

A C E

M A and C

Z

All of the above

12. Multi-Step Problem

Multiple Choice Use the following

choices to complete the proofs that ABE DBC and AED CDE. Given: B is the midpoint of EC and AD.

A B C D E

B A F

C

Given A Def. of midpoint Reflexive Prop. of Congruence E SSS Congruence Postulate SAS Congruence Postulate

C B

D

Chapter 4

E D

a. Prove that b. Prove that c. Prove that

ADF ACD BCD

ADB. AED. FED.

Geometry 23

Copyright © McDougal Littell Inc. All rights reserved.

Georgia Standardized Test Practice Workbook

LESSON

4.4

GA QCC: 1, 6, 14, 15, 16

Standardized Test Practice

For use with pages 220­227

GHSGT: 4, 22

TEST TAKING STRATEGY

Do not panic if you run out of time before answering all of the questions. You can still receive a high test score without answering every question.

5. Multiple Choice

1. Multiple Choice A B C D E

Which postulate or theorem can be used to prove that ABC BAD? SSS SAS A ASA AAS none of the above

C D

You are given the following information about GHI and EFD. II. IV. H GH F EF

G E I. III. I D V. GI ED

B

Which combination cannot be used to prove that GHI EFD?

A C E

V, IV, II III, V, I none of the above

B D

II, III, V V, IV, I

2. Multiple Choice

E

Which postulate or theorem can be used to prove that EFG IHG?

6. Multiple Choice

G H

F

Given that X D, and DE XW, what is the third congruence needDEC by ASA? ed to prove that XWY Y W C C

B D

A

I

Y W

E E

C E

A D

SSS AAS

B E

SAS C ASA none of the above

none of the above

7. Multiple Choice

3. Multiple Choice

What is the third congruence needed to prove that ABD CBD by AAS? AB BC ABD CBD AD DC DBA CDB A B or C

B

Given that G E and I D, what is the third congruence needed to prove that GHI EFD by AAS? H HI F FD

B D

A C E

HI ED

ED GI

A B C D E

none of the above

8. Multi-Step Problem

D C A C E O N

In the diagram, AB CD, CB DE, and AB CD.

B D

4. Multiple Choice

What is the third congruence needed to prove that MNQ PNO by ASA? Q P M MNQ PNO M O M P Q QN NO

Chapter 4

A B C D E

ABC CDE. b. Prove that C is the midpoint of AE.

a. Prove that

P

24 Geometry

Georgia Standardized Test Practice Workbook Copyright © McDougal Littell Inc. All rights reserved.

LESSON

4.5

GA QCC: 14, 15, 16

Standardized Test Practice

For use with pages 229­235

GHSGT: 22

TEST TAKING STRATEGY

Make sure that you are familiar with the directions before taking a standardized test. This way, you do not need to worry about the directions during the test. Multiple Choice In Exercises 5­16, use

the choices below to complete the proof that AG FE.

A B C D E

1. Multiple Choice

Which postulate or theorem can be used to prove that the triangles are congruent given M is the midpoint of KQ and KL PQ? SSS SAS ASA AAS AAA

K M P

A B C D E

Alternate Interior Angles Theorem ASA Congruence Postulate s are Corresp. parts of . Vertical Angles Theorem Definition of Congruence

B C F G

L

Q A

2. Multiple Choice

Which statement correctly describes the congruence of the triangles in Exercise 1? KML KLM KML KLM KML PQM PQM QMP PMQ PQM

E

A B C D E

Statements

a.

Reasons

a. Given

3. Multiple Choice

After proving the triangles congruent in Exercise 1, what reason could you give to prove KL PQ? Vertical Angles Theorem Reflexive Prop. of Congruence s are Corresp. parts of . ASA Definition of midpoint

A B

A B C D E

b. c. d. e. f. g. h. i. j. k.

AB GC, GB EC, AG BE, GF FC, AGB FEC BFG EFC BGF ECF BGF ECF BG EC ABG FGB m ABG m FGB, m BGF m ECF m ABG m ECF ABG ECF ABG FCE AG FE 1 3 and 2

b. 5. c. 6. d. 7. e. 8. f. 9. g. 10. h. i. j. k.

Sub. prop. of equality

11. 12. 13.

4. Multiple Choice

You want to prove BC AF. As a first step, which pair of triangles would F you prove congruent? ADF CDB ADF EDF BCD FED B or C Any of the above

14. Multi-Step Problem a. Prove that

In the diagram, 4.

B C

2

D

C

A B C D E

E

AGC AGE. b. Prove that BCG FEG. c. Prove that

Chapter 4

A

1 3

G

4

D

F

E

CDG

EDG.

Copyright © McDougal Littell Inc. All rights reserved.

Geometry

Georgia Standardized Test Practice Workbook

25

LESSON

4.6

GA QCC: 10, 16, 17

Standardized Test Practice

For use with pages 236­242

TEST TAKING STRATEGY

Avoid spending too much time on one question. Skip questions that are too difficult for you, and spend no more than a few minutes on each question.

6. Multiple Choice A

x

11 3x 1

1. Multiple Choice A B C D E

What is the value of x?

Solve for x and y.

y

3 5 7 9 11

B

2x 8

C D

45 3x 4 5x 2

2. Multiple Choice

What is the length of a leg?

A C E

E

x y x y x y x x

120, 60 60, 60 30, 120 120, y 30 60, y 120

x

3 12 19

B D

17 13

7. Multiple Choice

7x 8

Solve for x and y. 55 110 110 145 145

z x y w

35

A B C

3. Multiple Choice

What are the values of x

and y?

A B C D E

D E

x x x x x

70, y 55, y 70, y 70, y 55, y

x x x x x

72.5, y 72.5 35, y 35 35, y 110 55, y 55 110, y 35

x

35

8. Multiple Choice

y

Use the diagram in Exercise 7 to solve for w and z. w w w 145, z 70 110, 70 70, z 55

B D

A C E

w w

110, z 145, z

55 55

4. Multiple Choice A B C D E

What is the value of x?

9.

30 60 90 100 Cannot be determined

Quantitative Comparison

Use the diagram B 3 to find the 30 2 missing values. C Choose the stateA 1 4 ment below that D F is true about E the given number. A The value in column A is greater. B The value in column B is greater. C The two values are equal. D The relationship cannot be determined from the given information. Column A m 1 Column B m 3

x

5. Multiple Choice

Choose the reason the trian-

gles are congruent.

Chapter 4

A B C D E

SSS SAS AAS ASA Cannot be proven congruent

Geometry

Georgia Standardized Test Practice Workbook

26

Copyright © McDougal Littell Inc. All rights reserved.

LESSON

4.7

GA QCC: 14, 42, 43, 46

Standardized Test Practice

For use with pages 243­250

GHSGT: 25

TEST TAKING STRATEGY

Staying physically relaxed during the SAT is very important. If you find yourself tensing up, put your pencil down and take a couple of deep breaths. This will help you stay calm.

6. Multiple Choice A B C D E

1. Multiple Choice

An isosceles right triangle has a vertex at 0, 0 and another at 0, 8 . If its legs are 8 units, what point below might be the third vertex? 8, 0 0, 8 All of the above

B D

What are the coordinates of the midpoint M? 40, 30 60, 40 30, 80 60, 30 30, 40

10 y N(30, 80)

Q(60, 80)

A C E

8, 0 A or B

M

2. Multiple Choice

A rectangle with sides of 3 units and 6 units is placed on a coordinate plane. If one vertex is at 0, 0 , which set of points could be the other vertex points? 0, 6 , 6, 3 , 3, 6 3, 0 , 0, 6 , 3, 6 3, 0 , 3, 0 , 0, 3, 6 , 0, 6, 3, 6 6

P(0, 0) R(30, 0)

10 x

A B C D E

Quantitative Comparison

In Exercises 7 and 8, use the diagram below. Choose the statement below that is true about the given value.

A B C D

All of the above

3. Multiple Choice

A right triangle has legs of 8 units and 10 units. Use a coordinate plane to solve for the hypotenuse. 18 80

B E

The value in column A is greater. The value in column B is greater. The two values are equal. The relationship cannot be determined from the given information.

y

A D

4 5 3 2

C

2 41

A(0, 6)

B(4, 6) C (6, 4)

4. Multiple Choice

A rectangle with length h and width k is placed in a coordinate plane with one vertex at 0, 0 . What is a possible point for the vertex diagonal to 0, 0 ? 0, h h, k

B E

A D

h, 0 h, 0

C

0,

k

1

O(0, 0)

1

D(6, 0)

x

5. Multiple Choice

Use the diagram in Exercise 6 to find the length of MP. M is the midpoint of PQ. 25 30

B E

Column A

7. 8.

Column B

Chapter 4

AD OB

BC

CD OC

A D

50 125

C

40

Copyright © McDougal Littell Inc. All rights reserved.

Geometry

Georgia Standardized Test Practice Workbook

27

LESSON

Chapter 5

5.1

GA QCC: 1, 15, 17, 18, 46

Standardized Test Practice

For use with pages 264­271

GHSGT: 4, 29

TEST TAKING STRATEGY

Make sure that you are familiar with the directions before taking a standardized test. This way, you do not need to worry about the directions during the test.

3. Multiple Choice

1. Multiple Choice

In the diagram, WY is the perpendicular bisector of AB. What is the value of x?

A

Y

7x 4 5x 6

and OP

In the diagram, KM PQ. Find PQ.

O

OQ,

A B

10

8 10 12 13 15

31 2 16 10 5

N

13

B C D

L K M

8

C D E

P

A

W

3x

10 B

E

Q

2. Multiple Choice

Which diagram below allows you to conclude that C is on the perpendicular bisector of AB?

C

4. Multiple Choice A

A

In the diagram, in Exercise 3, KM bisects OKQ. Find LM. 8 13

B E

10 15

C

12

I.

II.

D

Quantitative Comparison

C A P B B C P

In Exercises 5 and 6, choose the statement below that is true about the given values.

A B C D

The value in column A is greater. The value in column B is greater. The two values are equal. The relationship cannot be determined from the given information. Given: MN is the perpendicular bisector of AB.

N

5z 4y 1

3 x 2

III.

A

P

B

A C E

I only III only none of these

B D

II only II and III

6

2y

O

8 3z 12

7

A

2

M

1 x 2

B

5. 6.

Column A AB AM

Column B NB MO

28

Geometry

Georgia Standardized Test Practice Workbook

Copyright © McDougal Littell Inc. All rights reserved.

LESSON

5.2

GA QCC: 17, 18

Standardized Test Practice

For use with pages 272­278

GHSGT: 20

Chapter 5

TEST TAKING STRATEGY

1. Multiple Choice

Work as quickly as you can through the easier sections, but avoid making careless errors on easy questions.

5. Multiple Choice

Complete the statement so that it is true. "The point of concurrency of the ______ of a triangle is called the ______ of the triangle." perpendicular bisectors; incenter perpendicular bisectors; circumcenter angle bisectors; circumcenter angle bisectors; inscribecenter A and C

bisectors of

A B C D E

In the diagram, the angle ACE meet at point G. Find GD.

B A G

5

1 2 3 4 5

F

C

A B C D E

D

4

E

6. Multiple Choice 2. Multiple Choice

circumcenter of

A B C D E

In the diagram, P is the ABC. Find the value of x.

B

angle bisectors of Find NP.

A B

In the diagram below, the KLM meet at point N.

L

1 3 9 15 21

A D P F

10 25 20 31 15

K

25

O

E

C D

C

N

P

E

Q 40

M

Given: PB

3. Multiple Choice

15; PC

3x

6

7. Multi-Step Problem

The point of concurrency of the three perpendicular bisectors of an obtuse triangle is ? the triangle. always inside always on sometimes outside

B D

A city is planning a new recreational park. They want to locate the new park so that it is equidistant from three large apartment complexes. is looking for?

A C E

always outside sometimes inside

a. What term best describes the point the city b. The three apartment complexes would be

4. Multiple Choice

The point of concurrency of the three angle bisectors of a right triangle is ? the triangle. always inside always on sometimes on

B D

located at 4, 5 , 2, 1 , and 6, 1 on a coordinate plane. Plot the points and draw the perpendicular bisectors of the triangle formed.

c. What are the coordinates of the best posi-

A C E

always outside sometimes inside

tion for the new park?

d. If each unit on the coordinate plane is

1 mile, how far is each apartment complex from the park?

Copyright © McDougal Littell Inc. All rights reserved.

Geometry

Georgia Standardized Test Practice Workbook

29

LESSON

Chapter 5

5.3

GA QCC: 1, 15, 17, 18, 43, 46

Standardized Test Practice

For use with pages 279­285

GHSGT: 4

TEST TAKING STRATEGY

It is important to remember that your SAT score will not solely determine your acceptance into a college or university. Do not put added pressure on yourself to do well. If you are not satisfied with your SAT score, remember that you can take it again.

6. Multiple Choice

1. Multiple Choice

In the diagram, C is the centroid of XYZ, UY XZ, CW 3, and CZ 8. Find CX. 3 6 9 8 12

Z W U C Y X V

A B C D E

Complete the statement to make a true statement. "The three altitudes of an obtuse triangle ? intersect ? the triangle." always; inside sometimes; inside always; outside sometimes; outside never; outside

A B C D E

2. Multiple Choice A D

16 3

Use the diagram in Exercise 1. Find VZ.

B E

Quantitative Comparison

8

4 16

C

12

In Exercises 7­9, use the diagram below. Point C is the centroid of DEF, CH 6, GE 10, and GF 15. Choose the statement below that is true about the given value.

E

3. Multiple Choice A B C D

In the diagram in Exercise 1, if XU UZ, then UY is ? . an altitude a perpendicular bisector a median an angle bisector

E

D G C H

all of these

A B C D

I

F

The value in column A is greater. The value in column B is greater. The two values are equal. The relationship cannot be determined from the given information. Column A DE GC CE Column B DH CF CD

4. Multiple Choice

What are the coordinates of the centroid of a triangle whose vertices are A 3, 1 , B 7, 3 , and C 5, 7 ? 5, 11 3 6,

8 3

A D

B E

5, 16 3 6,

11 3

C

5, 2

5. Multiple Choice A B C D E

30

What is the area of

B

ABC?

50 48 51 42 320

A

Geometry 6 20 17

7. 8. 9.

16

C

Copyright © McDougal Littell Inc. All rights reserved.

Georgia Standardized Test Practice Workbook

LESSON

5.4

GA QCC: 17, 18, 43

Standardized Test Practice

For use with pages 287­293

GHSGT: 35

Chapter 5

TEST TAKING STRATEGY

Do not panic if you run out of time before answering all of the questions. You can still receive a high test score without answering every question.

5. Multiple Choice

1. Multiple Choice A B C D E

In the diagram, UV and WU are midsegments of XYZ. Find WX. 5 10 15 4 8

Z U

5

perimeter of

A B C

Use the diagram to find the L KLM.

X

W

Y

60 120 150 180 240

K B

15

O

25

P

V 8

D E

M

2. Multiple Choice

Use the diagram in Exercise

B E

6. Multiple Choice

Use the diagram below to

L

1 to find WU.

A D

find FG.

F K

5x 7

5 4

10 8

C

15

G E

12x 8

3. Multiple Choice

y

Find the coordinates of the endpoints of the midsegment parallel to AB.

B(4, 7)

A B C

4, 2 , 3, 4 3, 4 , 5, 5 3, 4 , 4, 7 4, 2 , 4, 7 4, 2 , 5, 5

A D

M

3 44

B E

6 7

C

22

C(6, 3)

1 1

D E

Quantitative Comparison

A(2, 1)

x

In Exercises 7 and 8, use the diagram below. BD, DF, and BF are midsegments of ACE. BC 10, AE 12. Choose the statement below that is true about the given value.

A B C D

4. Multiple Choice

Given the midpoints of a triangle are 7, 4 , 5, 6 and 8, 7 , which coordinates below are the vertices? 6, 9 , 5, 4 , 11, 6 5, 4 , 10, 5 , 6, 9 4, 3 , 10, 5 , 6, 9 4, 3 , 7, 9 , 11, 5 4, 3 , 6, 9 , 11, 6

The value in column A is greater. The value in column B is greater. The two values are equal.

A B

C

10

A B C D E

D

The relationship cannot be determined from the given information. Column A BD The perimeter of CDB

F 12

E

7. 8.

Copyright © McDougal Littell Inc. All rights reserved.

Column B BF The perimeter of DEF

Geometry 31

Georgia Standardized Test Practice Workbook

LESSON

Chapter 5

5.5

GA QCC: 1, 2, 15, 17, 18, 46

Standardized Test Practice

For use with pages 295­301

GHSGT: 4

TEST TAKING STRATEGY

1. Multiple Choice

Read each test question carefully. Always look for shortcuts that will allow you to work through a problem more quickly.

5. Multiple Choice

Use the diagram below to determine which statement is true.

I

60

Which statement below

y

is false?

m x

n z n

2

w

H

35

85

A

J

m x < m y m x m y > m w m y < m w m x < m w m w > m z Use the diagram to solve BC > AC.

B

4x 3x 2 5

B C D E

A B C D

m H < m J < m I HI < HJ < JI JI < HJ < HI HJ > HI

E

m I > m H

6. Multiple Choice

2. Multiple Choice A B C D E

Which is the shortest side?

B

45

the inequality AB

A B C D

AC AB BC A or C cannot be determined

x > 0 x < x < 0 x > 10 x > 4

A

4

C

6x 3

65

C

E

A

Quantitative Comparison

3. Multiple Choice

List the sides in order from

E

60

longest to shortest.

A B C D E

GF, EF, EG EG, GF, EF EF, EG, GF EF, GF, EG EG, EF, GF

G

In Exercises 7 and 8, use the diagram below. Choose the statement that is true about the given value.

B

40 35

40

F

A

D

C

A B C D

The value in column A is greater. The value in column B is greater. The two values are equal. The relationship cannot be determined from the given information. Column A AB BC Column B AD DC

Copyright © McDougal Littell Inc. All rights reserved.

4. Multiple Choice

A triangle has two sides that have lengths of 8 cm and 14 cm. Which length below could not represent the length of the third side? 7 cm 22 cm

Geometry

Georgia Standardized Test Practice Workbook

A D

32

B E

13 cm 15 cm

C

18 cm

7. 8.

LESSON

5.6

GA QCC: 17, 18

Standardized Test Practice

For use with pages 302­308

GHSGT: 29

Chapter 5

TEST TAKING STRATEGY

When checking your work, try to use a method other than the one you originally used to get your answer. If you use the same method, you may make the same mistake twice.

4. Multiple Choice

1. Multiple Choice

Use the diagram to determine which of the following is a possible length for AC.

A

15 50 45

Use the diagram below and the given information to choose the conclusion that is true.

A B

D

Given: AB ED AC > CD

A

E

m A > m D m D > m A m A > m E m B > m D m A < m E

E D C

C

B F

B

A D

10 15

B E

12 17

C

13

C D E

2. Multiple Choice

In the diagram, which of the following is not a possible measure for DCB?

C

5. Multiple Choice

Use the diagram and the Hinge Theorem to choose the inequality that correctly describes the restriction on the value of x.

10 60 50 10

35

A

15

D

13

B

3x

2

A D

27 20

B E

30 34

C

35

A

2x

6

x > 4 x < 2

B E

x < 4 x > 2

C

x <

8 3

3. Multiple Choice

Use the Hinge Theorem and the diagram below to choose the statement which must be true.

12 3 1 4 10 2

D

6. Multi-Step Problem a. Sketch an acute triangle ABC with

m A

45 and m C

55 . BCD. ABC?

b. Draw an exterior angle adjacent to BC

with vertex at C, and label it

c. Determine m BCD. d. What is the shortest side of

A B C D E

m 1 > m 3 m 1 m 2 m 1 > m 2 m 1 < m 2 m 4 > m 2

e. Use your diagram as a reference to write

the first statement of an indirect proof of "the measure of an exterior angle of a triangle is equal to the sum of the two nonadjacent interior angles."

Geometry

Georgia Standardized Test Practice Workbook

Copyright © McDougal Littell Inc. All rights reserved.

33

LESSON

6.1

GA QCC: 1, 2, 10, 18

Standardized Test Practice

For use with pages 322­328

GHSGT: 4, 29, 30

TEST TAKING STRATEGY

Do not panic if you run out of time before answering all of the questions. You can still receive a high test score without answering every question.

6. Multiple Choice A

1. Multiple Choice

Which figure below is a III.

Find m A.

A B 165 C

30

polygon? I.

Chapter 6

65 135 100 90 105

65

II.

B C

A C E

I only III only none of these

B D

II only I and III

D E

D

7. Multiple Choice

Find the value of x.

(5x 5) A (2x 10)

2. Multiple Choice

A polygon with 7 sides is .

B D

A B C D E

40 10 45 30 70

B

called a

A C E

?

D

nonagon heptagon decagon

dodecagon hexagon

55

C

3. Multiple Choice

An octagon has how many

8. Quantitative Comparison B E

sides?

A D

5 8

6 9

C

7

Choose the statement below that is true about the given value. Given: ABCF EDCF The value in column A is greater. The value in column B is greater. The two values are equal. The relationship cannot be determined from the given information.

A

80

1 y 2 F 100

A B C D

4. Multiple Choice

The figure below is a

?

A B C D E

.

convex hexagon convex heptagon concave heptagon concave hexagon concave pentagon The polygon below is best .

B

(

30

)

D

35

C

5. Multiple Choice

described as

A B C D E

34

?

2x

E

an equilateral pentagon an equiangular pentagon a regular pentagon an equilateral hexagon an equiangular hexagon

Geometry

Georgia Standardized Test Practice Workbook

Column A x

Column B y

Copyright © McDougal Littell Inc. All rights reserved.

LESSON

6.2

GA QCC: 1, 15, 17, 18, 19, 46

Standardized Test Practice

For use with pages 330­337

GHSGT: 4, 29, 30

TEST TAKING STRATEGY

If you find yourself spending too much time on one test question and getting frustrated, move on to the next question. You can revisit a difficult problem later with a fresh perspective.

6. Multiple Choice

1. Multiple Choice

lelogram must be

A C E

Opposite angles of a paral? .

B D

complementary congruent B and C

supplementary A and C

What are the values of x and y?

5y

1

2x

4y

7

Chapter 6

3y

6

A 2. Multiple Choice

x x x

12, y 8, y 15, y

6 15 8

B D

x x

6, y 4, y

12 8

What are the values of the variables in parallelogram ABCD?

A 3x

120 C

C E

B

2y

7. Multiple Choice

D

Three coordinate points of a parallelogram are 2, 1 , 4, 4 , and 7, 4 . Find the fourth vertex. 5, 1 5, 7

B E

A A C E

2, 7 1, 7

C

5, 4

x x x

40, y 60, y 40, y

60 20 30

B D

x x

30, y 20, y

40 60

D

8. Quantitative Comparison

3. Multiple Choice A C E

What is the length of LP?

L

20

Use the information given. Choose the statement below that is true about the given value. The value in column A is greater. The value in column B is greater. The two values are equal. The relationship cannot be determined from the given information.

4 8 20

B D

5 10

M P

A B

4

5

C

N

O

D

4. Multiple Choice

In the parallelogram in Exercise 3, what is the length of MN if the perimeter is 70 units? 20 units 10 units 50 units

B D

Given: ABCD, DEFG, and FHIJ are parallelograms.

C G B D F I H

A C E

15 units 30 units

5. Multiple Choice A B C D E

Which statement is not always true about parallelogram WXYZ? VX XY WY VZ WZ YZW

Z Y W V X

A

E

J

Column A m C

Column B m E

WXY XZ WXZ

XZY

Geometry

Georgia Standardized Test Practice Workbook

Copyright © McDougal Littell Inc. All rights reserved.

35

LESSON

6.3

GA QCC: 6, 17, 18, 19, 46

Standardized Test Practice

For use with pages 338­346

GHSGT: 4, 29, 30

TEST TAKING STRATEGY

Read each test question carefully. Always look for shortcuts that will allow you to work through a problem more quickly.

4. Multiple Choice A C E

C

1. Multiple Choice

Which additional piece of information do you need to prove ABCD is a parallelogram? AB AD AB DC BC DC

D A E B

What value of x will make the quadrilateral a parallelogram? 5 50 60

B D

10 40

(x

20) 3x

A

Chapter 6

B C D E

A or B B or C

5. Multiple Choice

Given that AED CEB, ABCD would be a parallelogram because ? .

A E B C D

2. Multiple Choice

WXYZ is a quadrilateral. Which information would not allow you to conclude that WXYZ is a parallelogram? WX W WX WZ WZ ZY, WZ Y, ZY, WZ XY, WX X XY ZY XY Z

A B C D E

A B C D E

both pairs of opposite sides are parallel the diagonals bisect each other both pairs of opposite sides are congruent both pairs of opposite angles are congruent one pair of opposite sides is congruent and parallel

XY, WZ XY

3. Multiple Choice

To prove that ABCD is a parallelogram, you would have to first prove ACD CAB using the ? .

A B

6. Multi-Step Problem

Consider the four points A 5, 4 , B 6, 2 , C 3, 1 , and D 8, 5 . showing that opposite sides are parallel.

D

C

a. Show that ABCD is a parallelogram by b. Show that ABCD is a parallelogram by

A B C D E

SAS Congruence Postulate SSS Congruence Postulate AAS Congruence Postulate ASA Congruence Postulate none of these

showing that opposite sides are congruent.

c. Show that ABCD is a parallelogram by

showing that the diagonals bisect each other. Label the intersection of diagonals AB and CD point E.

36

Geometry

Georgia Standardized Test Practice Workbook

Copyright © McDougal Littell Inc. All rights reserved.

LESSON

6.4

GA QCC: 17, 18, 19

Standardized Test Practice

For use with pages 347­355

GHSGT: 30

TEST TAKING STRATEGY

When checking your work, try to use a method other than the one you originally used to get your answer. If you use the same method, you may make the same mistake twice.

6. Multiple Choice

1. Multiple Choice

What special type of quadrilateral has the vertices A 2, 1 , B 2, 3 , C 2, 1 , and D 2, 3 ? rhombus rectangle none of these WXYZ is a rhombus. What

(3x

In rectangle ABCD, AB 1 x 6 and CD 5x 2. Find the 2 2 value of x. 4 2

B E

3 4 3 3

A C E

B D

square parallelogram

A D

C

5

Chapter 6

7. Multiple Choice

2. Multiple Choice

is the value of x?

(8x (5x 3) 6) 12)

The perimeter of a square MNOP is 72 inches, and NO 2x 6. What is the value of x? 15 9

B E

A D

12 18

C

6

8. Multiple Choice B E

KLMN is a rectangle. Find the values of x and y.

N

3y 21

A D

9

2 3

3 1

C

4

M

5y (2x 10) 11

3. Multiple Choice

In the diagram below, PQRS is a rhombus. What are the values of x and y? x x x x x

5 3,

K

L

A C

x x x

50, y 40, y 50, y

16 16 4

B D

x x

40, y 50, y

5 5

A B C D E

y

4 2 4 6 6

x S

5

P

5, y 10, y 5, y 10, y

E

y Q

2x

8

R

4. Multiple Choice

rectangle must A bisect each other

C E

The diagonals of a ? .

B D

Quantitative Comparison In the diagram, ACEG is a D rhombus, BDFH is a rectangle, and B ACE is an I equilateral A E triangle. For Exercises 9 and 10, choose a statement below that is true about the given value. F H

A B C D

C

be perpendicular A and B

The value in column A is greater. The two values are equal.

G

be congruent A and C

The value in column B is greater. The relationship cannot be determined from the given information. Column B m ICD GF

Geometry 37

5. Multiple Choice A C E

If a quadrilateral has four equal sides, then it must be a ? . rectangle rhombus B and C

B D

square A and B

9. 10.

Column A m BAI BC

Copyright © McDougal Littell Inc. All rights reserved.

Georgia Standardized Test Practice Workbook

LESSON

6.5

GA QCC: 17, 18, 19

Standardized Test Practice

For use with pages 356­363

GHSGT: 30

TEST TAKING STRATEGY

Staying physically relaxed during the SAT is very important. If you find yourself tensing up, put your pencil down and take a couple of deep breaths. This will help you stay calm.

5. Multiple Choice A C E

N M

1. Multiple Choice

and NM are

A

?

In trapezoid KLMN, KL .

K L

Find the length of KL in the trapezoid below. 22 13 27

B D

legs bases consecutive angles diagonals none of these

4 17

H N

K

4x 5x

1 2 27

L I M

Chapter 6

B C D E

6. Multiple Choice

2. Multiple Choice

In the isosceles trapezoid

A

110

ABCD, find m B.

A B C D E

What special type of quadrilateral has the vertices A 6, 3 , B 2, 5 , C 3, 2 , and D 5, 6 ? square rhombus kite

B D

110 55 70 60 140

B

D

A C E

C

rectangle trapezoid

7. Multiple Choice

3. Multiple Choice

Which statements below must be true if ABCD is an isosceles trapezoid with a leg AD? I. AB DC BC III. AB IV. AD

B D

The midsegment of a trapezoid is 9 cm long. What choice below is not a possible choice for the lengths of the bases? 2, 16 6, 12

B E

A D

5, 4 5, 13

C

8, 10

DC BC I and IV II and IV

8. Quantitative Comparison

II. AD

A C E

I and III II and III I, II, and III

In the diagram, DEFG is a kite. Choose the statement below that is true about the given value. The value in column A is greater. The value in column B is greater. The values are equal. The relationship cannot be determined with the given information. Column B y

D

2y

A B C D

4. Multiple Choice A B C D E

ABCD is a trapezoid. Find the length of midsegment EF. 5 11 16 8 22

11

A E

13

Column A x

B

7

D F 9

G x F

x

E

5 2

5

C

38

Geometry

Georgia Standardized Test Practice Workbook

Copyright © McDougal Littell Inc. All rights reserved.

LESSON

6.6

GA QCC: 17, 18, 19

Standardized Test Practice

For use with pages 364­370

GHSGT: 29

TEST TAKING STRATEGY

Avoid spending too much time on one question. Skip questions that are too difficult for you, and spend no more than a few minutes on each question.

5. Multiple Choice

1. Multiple Choice

most specifically a

A B C D E

The quadrilateral below is ? .

Which statements below are always true about a rectangle? I. Both pairs of opposite angles are congruent. II. The diagonals are perpendicular.

Chapter 6

rhombus rectangle kite parallelogram trapezoid

III. Both pairs of opposite sides are congruent.

A D

I I and III

B E

II

C

III

2. Multiple Choice

A quadrilateral with at least two sides parallel and two congruent sides might be ? . a rhombus an isosceles trapezoid a kite A or B none of these

none of these

6. Multiple Choice

A B C D E

Which statements below are always true about a trapezoid? I. Exactly one pair of opposite sides are congruent. II. Exactly one pair of opposite sides are parallel.

III. The diagonals are congruent.

A D

3. Multiple Choice

What kind of quadrilateral would meet the conditions of the diagram? ABCD is not drawn to scale. kite rhombus trapezoid square parallelogram

D C A B

I I and II

B E

II

C

III

none of these In the diagram, DEFG ABC is regular.

B

A B C D E

7. Multi-Step Problem

is a rectangle and

D

E

4. Multiple Choice A C E

What value of x would make quadrilateral ABCD a trapezoid? 30 25 10

(5x D 20)

A B

G

F

C

2 3y

B D

20 35

A

3x

a. If GE

10y 2 and DF the value of y.

12, find

b. If the midsegment of trapezoid DECG is 5

C

inches, DE 3x 2, and GC find the value of x.

c. Prove that

8x

3,

ADG

CEF.

Copyright © McDougal Littell Inc. All rights reserved.

Geometry

Georgia Standardized Test Practice Workbook

39

LESSON

6.7

GA QCC: 1, 2, 18, 19, 32, 37

Standardized Test Practice

For use with pages 372­380

GHSGT: 4, 20, 26, 27, 35

TEST TAKING STRATEGY

1. Multiple Choice A C

One of the best ways to prepare for the SAT is to keep up with your regular studies and do your homework.

6. Multiple Choice A

2

Find the area of a square with a perimeter of 30 cm. 225 cm2 30 cm

2

The area of the kite is 160 square inches. Find the length of BD. 10 in. 20 in. 8 in. 16 in. 32 in.

C D

10

B D

15 cm2 56.25 cm

A

B C

Chapter 6

E

60 cm2 Find the area of

C

2. Multiple Choice A B C D E

ABC.

D E

B

17.5 square units 7.5 square units 30 square units 15 square units 9 square units

5

7 6

7. Multiple Choice

Find the area of a trapezoid with vertices at A 0, 0 , B 2, 4 , C 6, 4 , and D 9, 0 . 26 square units 52 square units 18 square units

B D

A

3

B

A C E

13 square units 36 square units

3. Multiple Choice

Find the base length of a triangle with an area of 52 cm2 and a height of 13 cm. 8 cm 2 cm

B E

A D

16 cm 26 cm

C

4 cm

8. Multi-Step Problem

A doll house is sketched below. There is no back to the house or roof, but there are sides to both. windows and the doors).

4. Multiple Choice

Find the area of parallelogram EFGH.

E F

15 8 14

a. Find the area of the walls (including the b. Find the area of the window openings.

The window above the door consists of 5 congruent isosceles triangles.

c. Find the area of the roof.

H

G

A C E

75 square units 120 square units 60 square units

B D

112 square units 56 square units

1.5 ft 6 in. 3 in. 6 in. 3 in.

5 ft 1.5 ft 6 in. 3 in. 6 in. 3 in. 6 ft

1.6

ft

2 ft 2 ft 4 in. 2 in.

5. Multiple Choice A C E

2 3

The area of the rectangle is 60 square units. Find the value of x.

B D

40 7

2x

1

1 x 2

59 8

40

Geometry

Georgia Standardized Test Practice Workbook

Copyright © McDougal Littell Inc. All rights reserved.

CHAPTER

6

? .

A C E

Cumulative Standardized Test Practice

For use after Chapters 1­6

1. Multiple Choice

XY and WY intersect at

B D

6. Multiple Choice A B C D E

What is the converse of "If there is ice on the lake, then it is cold?" If there is not ice on the lake, then it is not cold. If it is cold, then there is ice on the lake. If it is not cold, then there is not ice on the lake. There is ice on the lake if and only if it is cold. none of these

Chapter 6

point X point W none of these

point Y WX

2. Multiple Choice

Point B is between A and C. Use the Segment Addition Postulate to solve for x when AB 5x 2, AC 12x 7, and BC 26. 1 4

B E

A D

2 5

C

3

7. Multiple Choice

3. Multiple Choice

Find the measure of

ABD.

A B C D E

Which of the following is true about the conditional statement. "If m 1 40 and the m 2 50 , then the angles are complementary." The statement is true.

30 60 90 120 150

I.

A

120 30

II. The biconditional is true.

D C

III. The converse is true.

A D

I I and II

B E

II I and III

C

III

B

4. Multiple Choice

AB bisects

C

(4x

CAD. Find

8. Multiple Choice

In HIJK, HK

H

IJ. What is

I

7x 2

the value of x.

A B C D E

the value of x?

A

2 4 6 8 10

A

1 2 2.5 3 3.5

5x

2)

B C D

3

B

(3x 6)

K

J

D

E

5. Multiple Choice A B C D E

Find the value of y.

9. Multi-Step Problem

30 35 85 22 55

(3y 5) 85

Let p be "You stay up late," q be "You are tired" and r be "You are cranky."

a. Write p q in words. b. Write q r in words. c. Write the contrapositive of p q in words

and symbols.

d. Writing

Use the Law of Syllogism and the statements from parts (a) and (b) to write a new conditional statement.

Copyright © McDougal Littell Inc. All rights reserved.

Geometry

Georgia Standardized Test Practice Workbook

41

CHAPTER

CONTINUED

6

Cumulative Standardized Test Practice

For use after Chapters 1­6

10. Multiple Choice

Solve x 12 24, then choose the property that applies to the required step. Substitution property of equality. Division property of equality. Subtraction property of equality. Distributive property of equality. Reflexive property of equality.

14. Multiple Choice

Find the value of x when

t

(4x 65 3)

a b.

A B C D E

15 16 17 18 19

A B C

a b

Chapter 6

D E

15. Multiple Choice 11. Multiple Choice A D

Two angles are supplementary. If m 1 is 67 , what is m 2? 67 134

B E

What value of a would make lines x and y parallel? 29 36 7 14 58

t

5a 145

A B C D E

23 113

C

46

x y

12. Multiple Choice A B C D E

Solve for x and y. 24 412 3 31.67 5(x 30 28.3 4 and 5

(3y 4) 15)

x x x x x

21.25, y 25, y 22, y 25, y 24, y

16.

3(x 10)

Choose the statement below that is true. A The value in column A is greater.

B C D

Quantitative Comparison

The value in column B is greater. The two values are equal. The relationship cannot be determined from the given information. Column A Slope of the line 5x 2y 12 Column B Slope of the line perpendicular to y 2 x 6 3 1.

13. Multiple Choice

In the diagram, are what type of angles?

1 3 2 4 5 7 6 8

A B C D E

corresponding angles alternate interior angles alternate exterior angles consecutive interior angles consecutive exterior angles

17. Multiple Choice A B C D E

Find the measure of

32 1

32 35 90 58 55

35

42

Geometry

Georgia Standardized Test Practice Workbook

Copyright © McDougal Littell Inc. All rights reserved.

CHAPTER

CONTINUED

6

Z

Cumulative Standardized Test Practice

For use after Chapters 1­6

18. Multiple Choice

X

15

Given X C, find the value of x.

A

A and

22. Multiple Choice

A right triangle has legs of 24 units and 18 units. The length of the hypotenuse is ? . 15 units 45 units 32 units

Chapter 6

B D

A

35

30 units 15.9 units

C E C

Z

Y

(5x

15)

B

C

A D

25 30

B E

27 35

29

23. Multiple Choice

In the diagram, CD is the perpendicular bisector of AB. What is the value of x? 2.43 3 2.5 2 7

A D 15 B

3(x 8) 7x 4

19. Multiple Choice

Which postulate or theorem can be used to prove that ABC DCB? SSS SAS ASA AAS none of these

A C B D

A B C D E

C

A B C D E

24. Multiple Choice

In the diagram, AD bisects CAE. Which statements below are true? BG BC I II III I and III none of these In the diagram, C is the cirXYZ. Find the value of XC.

Y M C X

2x 15

I.

20. Multiple Choice

GF FE DE

A F B G

C

Which postulate or theorem can be used to prove that MNO KNL if MO LK? SSS SAS HL AAS

O N K M L

II.

A B C D E

III. CD

A B C D E

D

E

none of these What are the values of x 5 5 4 19 19

3y 37 7

21. Multiple Choice

25. Multiple Choice

and y?

A B C D E

cumcenter of 37, y 106, y 54, y 106, y 37, y

x

2y 12

x x x x x

A B C D E

1 2 3 4 5

O

3x

10

N

Z

Copyright © McDougal Littell Inc. All rights reserved.

Geometry

Georgia Standardized Test Practice Workbook

43

CHAPTER

CONTINUED

6

Cumulative Standardized Test Practice

For use after Chapters 1­6

26. Multiple Choice

In the diagram, BD and BF are midsegments of ACE. Find BD and CE.

C B D

29. Multiple Choice

What are the values of x 8 8 4

36 3y 6 2(y 1) 3x

and y?

A B C

x x x x x

12, y 10, y 12, y 8, y 10, y

Chapter 6

A

6

D E

4 7

F 15

E

30. Multiple Choice A B C D E

BD BD BD BD BD

7.5, CE 7.5, CE 7.5, CE 15, CE 8, CE

18 6 12 6 12

What value of x will make the quadrilateral a parallelogram? 5 10 15 20 25

(3x 20) (5x )

A B C D E

27. Multiple Choice

Use the Hinge Theorem and the diagrams below to choose the statement which must be true.

4 3 15 17 2 1

31. Multiple Choice

The perimeter of a square is 68 m. If one side is represented by 3x 2, what is the value of x? 3 6

B E

A D

5 10

C

4

Quantitative Comparison

A C E

m 1 > m 2 B m 1 > m 3 D m 4 > m 2

m 1 < m 3 m 2 < m 4

In Exercises 32 and 33, choose the statement below that is true about the given statement.

A B

The value in column A is greater. The value in column B is greater. The two values are equal. The relationship cannot be determined from the given information. Column A

A

10 8

28. Multiple Choice A B C D E

Find the value of x.

(5x 28) 95 (3x 10) 75

C D

15 16 18 19 21

Column B

B

9

E

9 9.2

10

F

8

D

C

H

12

G

32. 33.

44 Geometry

Georgia Standardized Test Practice Workbook

The area of ABCD The perimeter of ABCD

The area of EFGH The perimeter of EFGH

Copyright © McDougal Littell Inc. All rights reserved.

LESSON

7.1

GA QCC: 38, 40, 41

Standardized Test Practice

For use with pages 396­402

GHSGT: 22

TEST TAKING STRATEGY

Sketch graphs or figures in your test booklet to help you solve the problems. Even though you must keep your answer sheet neat, you can make any kind of mark you want in your test booklet.

4. Multiple Choice

1. Multiple Choice

Which of the statements

below are true? I. Rigid transformations are isometries. II. Three types of transformations are reflections, rotations, and transcriptions. III. Isometries preserve distances between points.

A C E

Name the type of transformation and the coordinates corresponding to point A .

y

A

B

I II and III None of these

B D

I and II I and III

A B

C

1 1 x

reflection in line x reflection in line x reflection in line x translation in line x

1, 3, 4 0, 3, 4

Chapter 7

2. Multiple Choice

Which of the following is

B

C D E

rotation about 1, 0 , 6, 4 1, 6, 4 1, 6, 4

not an isometry?

A

Quantitative Comparison

C D

In Exercises 5 and 6, use the isometry of the kite to find the value of the variables. Choose the statement below that is true about the values.

A

The value in column A is greater. The value in column B is greater. The two values are equal. The relationship cannot be determined from the given information.

B

1 z 2

E

None of these Name the preimage of MN.

M L C B D F E A N P Q O

B C D

3. Multiple Choice A B C D E

AB BC CD DF FA

20 2y

2 w 5

N (3x

10 110 O

35)

A

95

C

Q

D

P

5. 6.

Column A x w

Column B y z

Copyright © McDougal Littell Inc. All rights reserved.

Geometry

Georgia Standardized Test Practice Workbook

45

LESSON

7.2

GA QCC: 38, 40, 41, 46

Standardized Test Practice

For use with pages 404­410

GHSGT: 22

TEST TAKING STRATEGY

1. Multiple Choice

Work as quickly as you can through the easier sections, but avoid making careless errors on easy questions.

6. Multiple Choice

Which choice below is a reflection of the figure in line h?

h

B 6, AC

A D

Given that A 2, 4 and 2 , find point C on the x-axis so that BC is a minimum.

B E

0, 4 4, 0

0, 5 5, 0

C

3, 0

A

B

7. Multiple Choice C D

Given that the diagram shows a reflection in line m, find the values of x and y. x x x x x 10, y 10, y

5 2, 5 2, 3 2

A E

12

1 x 2

None of these If A 3, 2 is reflected in 3, then the coordinates of A are

B E

B C

4

3 2

y y

m

8y 5 13

2. Multiple Choice

Chapter 7

the line x ? .

A D

D E

4

13 8

6, y

0,

2 3, 2

3, 0, 1

2

C

3, 1

8. Multi-Step Problem

y

B(5, 6)

3. Multiple Choice

in the line y are ? .

A C E

If B 2, 1 is reflected 3, then the coordinates of B

B

A(1, 4)

4, 5 2, 2, 7 1

2, 5 8, 5

1 1

D

C(3, 1)

x

a. Draw and label 4. Multiple Choice A B C D E

Use the diagram below to complete the statement: GHI ? . NOP KPO LKP KLM ONM

F J E G H I P O N L K M

reflection of

c. Draw and label

A B C , which is the ABC in the x-axis.

b. Name the image of AB.

reflection of x 2.

A B C , which is the ABC in the y-axis. ABC in the line

d. Draw the reflection of

e. Find the midpoint of AA .

5. Multiple Choice A C E

46

How many lines of symmetry does the polygon have? 0 2 4

Geometry

Georgia Standardized Test Practice Workbook Copyright © McDougal Littell Inc. All rights reserved.

B D

1 3

LESSON

7.3

GA QCC: 1, 38, 40, 41, 46

Standardized Test Practice

For use with pages 412­420

GHSGT: 4, 22

TEST TAKING STRATEGY

1. Multiple Choice

Make sure that you are familiar with the directions before taking a standardized test.

5. Multiple Choice

Use the figure below to determine which segment represents a 90 clockwise rotation of AB about P. BC CD DE AH HG

A P H G F E D B C

Find the angle of rotation

A B

that maps ABC onto A B C .

A B C D E

A B C D E

60 30 120 180 None of these

A

60

C C C

m A B B k

6. Multiple Choice 2. Multiple Choice A B C D E

Which description of a rotation would map the figure below onto itself? clockwise 45 clockwise 90 clockwise 180 counterclockwise 45 none of these

7.

ABC has vertices A 2, 1 , B 3, 2 and C 5, 1 . What are the coordinates of the vertices of A B C after a rotation of 180 clockwise about the origin? A 2, A A A 2, 2, 2, 1 ,B 1 ,B 1 ,B 3, 3, 3, 2 ,C 2 ,C 2 ,C 5, 1 5, 1

Chapter 7

A B C D E

5, 5, 1

1

A 2, 1 , B 3, 2 , C 5, 1 1 , B 3, 2 , C

Multiple Choice Use the figure below for Exercises 3 and 4. State the segment or triangle that represents the image.

A I H M L G F B N Q P J O K E D C

Quantitative Comparison

Use the diagram below to find the value of each variable in the rotation of the polygon about point P. Choose the statement below that is true about the values. The value in column A is greater. The value in column B is greater. The two values are equal. The relationship cannot be determined from the given information.

y

6 12

A B C D

m

1 w 5

3. A 90 clockwise rotation of HI about Q. A D

8

LF BJ

B E

HL JD

C

KO

96

x P

2 z 3

25

4. A 90 counterclockwise rotation of QO about P. A D

QN OK

B E

MQ LM

C

LP

Column A y

Column B z

Copyright © McDougal Littell Inc. All rights reserved.

Geometry

Georgia Standardized Test Practice Workbook

47

LESSON

7.4

GA QCC: 38, 40, 41, 42, 46

Standardized Test Practice

For use with pages 421­428

GHSGT: 22

TEST TAKING STRATEGY

If you find yourself spending too much time on one test question and getting frustrated, move on to the next question. You can revisit a difficult problem later with a fresh perspective.

4. Multiple Choice

( 6, 4) P

1. Multiple Choice

The translation "5 units to the left and 3 units up" in coordinate notation would be ? . x, y x x, y x x, y x x, y x x, y x 5, y 5, y 5, y 3, y 3, y 3 3 3 5 5

Name the vector that describes the translation.

y

A B C D E

S

( 3, 3) 3 Q P (0, 1) ( 9, 1) (3, 0) R 1 Q x ( 4, 0) S R ( 3, 2) (2, 3)

2. Multiple Choice

Choose the notation below that describes the translation.

y

A C E

6, 3, 6 6, 3

3

B D

6, 3 3, 6

Chapter 7

5. Multiple Choice

1 1 x

The coordinates of JKL are J 1, 2 , K 2, 1 , and L 2, 1 . The component form of MN is 3, 4 . What are the coordinates of J K L after the translation using MN ?

\ \

A B C D E

x, y x x, y x x, y x x, y x x, y x

A

J J 2, J 2, J 2, J

4,

2 , K 1, 2 , K 1, 2 , K 1, 2 , K 1,

3 , L 5, 3 , L 5, 3 , L 5, 5 , L 5, 5 , L 5,

\

5 3 5 3 3

3, y 3, y 4, y 4, y 4, y

4 4 3 3 3

6.

B C D E

4,

2 , K 1,

3. Multiple Choice

\

Choose the correct name and component form of the vector shown. JH , 3, 4

\

Quantitative Comparison

A B C D E

JH ,

\

3, 4, 3,

4 3 4

H

J

A translation of A and B is described by NM 7, 2 . Solve for the indicated variable. Choose the statement below that is true about the value of the variable.

< >

JH ,

\ \

A B C D

The value in column A is greater. The value in column B is greater. The two values are equal. The relationship cannot be determined from the given information. Column A A 3, x , A 4, 4 Column B B y, 5 , B 10, 7

HJ , 3, 4 HJ ,

48

Geometry

Georgia Standardized Test Practice Workbook

Copyright © McDougal Littell Inc. All rights reserved.

LESSON

7.5

GA QCC: 38, 40, 41, 42, 46

Standardized Test Practice

For use with pages 430­436

GHSGT: 22

TEST TAKING STRATEGY

1. Multiple Choice

One of the best ways to prepare for the SAT is to keep up with your regular studies and do your homework.

3. Multiple Choice

Which two transformations were performed to obtain A B in the diagram?

B

y

Using the composition below, what are the coordinates of the endpoints of A B ?

B

A

1 1

A

x

Given: A 1, 3 , B 2, 5 Rotation: 90 counterclockwise about 1, 2 Reflection: in y x

A

A 0, 0 , B 1, A 2, 1 , B A 2, 1 , B A 0, 0 , B

2 4, 0 4, 0 1, 2

Chapter 7

B

B C

A

D E

A 2, 1 , B 4, 0

A B C D E

Rotate about the origin, then reflect in x y. Reflect in the x-axis, then translate parallel to x-axis. Reflect in the line x parallel to x 1. Reflect in the line y parallel to y 1. Translate parallel to x in line x 1. 1, then translate 1, then translate 1, then reflect

4. Multiple Choice

Translation 1 maps A to A . Translation 2 maps A to A . What translation below maps A to A ? 2, y 7, y 6 12 12 6 6

Translation 1: x, y x Translation 2: x, y x

A B C D E

x, y x x, y x x, y x x, y x x, y x

5, y 5, y 5, y 9, y 9, y

2.

Quantitative Comparison

Use the composition to locate points A and B . Choose the statement below that is true about the given lengths.

A B C D

5. Multiple Choice

Using the composition below, what are the coordinates of the endpoints of C D ? 2, 3 , D 3, 4 1

The value in column A is greater. The value in column B is greater. The two values are equal. The relationship cannot be determined from the given information.

Given: C

Rotation: 90 clockwise about origin Reflection: in x

A B C D E

C 5, C C C 5,

2 , D 6, 3 2 ,D 6, 3 2, 3

Given: A 4, 0 , B 2, 1 Translation 1: reflect in x 1 Translation 2: rotate 90 counterclockwise about (2, 1 Column A length of AA Column B length of BB

C 1, 2 , D 2, 3 1, 2 , D

1, 2 , D 2, 3

Copyright © McDougal Littell Inc. All rights reserved.

Geometry

Georgia Standardized Test Practice Workbook

49

LESSON

7.6

GA QCC: 38, 40, 41, 42

Standardized Test Practice

For use with pages 437­444

GHSGT: 22

TEST TAKING STRATEGY

1. Multiple Choice

Do not put added pressure on yourself to do well. If you are not satisfied with your SAT score, you can take it again.

5. Multiple Choice A

A frieze pattern is a pattern that extends to the left and right in such a way that the pattern can be mapped onto itself by a vertical translation. vertical reflection. horizontal translation. horizontal reflection. horizontal glide reflection.

Which design below is a frieze pattern with a classification of TV?

A B C D E

B C

D

In Exercises 2­7, use these classifications. T translation R 180 rotation H horizontal reflection V vertical reflection G horizontal glide reflection

2. Multiple Choice E

Chapter 7

6. Multiple Choice A

Which design below is a frieze pattern with a classification of TRVG?

Name the isometries that map the frieze pattern onto itself.

B C

A D

T TH

B E

TR TG

C

TV

D E

3. Multiple Choice

Name the isometries that map the frieze pattern onto itself.

7. Multi-Step Problem A D

TR TRHV

B E

TRH TRHVG

C

TH

Use the pattern below to create a frieze pattern with the given classifications.

4. Multiple Choice

Name the isometries

a. b. C E

that map the frieze pattern onto itself.

A B D

50

T TV THG TRHVG

Copyright © McDougal Littell Inc. All rights reserved.

TH TR TV

Geometry

Georgia Standardized Test Practice Workbook

THV THG

c. d.

LESSON

8.1

GA QCC: 1, 2

Standardized Test Practice

For use with pages 457­464

GHSGT: 4, 9, 19, 36, 40

TEST TAKING STRATEGY

Work as quickly as you can through the easier sections, but avoid making careless errors on easy questions.

3 ft . 18 in.

C

1 6

1. Multiple Choice A D

1 2

Simplify

B E

7. Multiple Choice

2

15 8

The ratio of side lengths of ABC to DEF is 3:1. Find the lengths of EF and AC.

A D 3 E

6

2. Multiple Choice A D

Simplify

B E

5m . 125 cm

C

F

25 0.25

0.04 40

4

B

18

C

A B C D E

EF EF EF EF EF

3, AC 6, AC 6, AC 6, AC 12, AC

3 5 9 5 3 5 21 3 17

3. Multiple Choice

The perimeter of rectangle ABCD is 72. The ratio of the lengths of the sides is 1:2. What are the lengths of the sides? 12 and 18 4.5 and 9 9 and 18

B D

A C E

12 and 24 6 and 12

Quantitative Comparison

4. Multiple Choice

The perimeter of HIJ is 36. The extended ratio of the sides is 2:3:7. Find the lengths of the sides. 3, 4, 9 8, 12, 28 2, 3, 7 Solve

B E B D

For Exercises 8 and 9, use the number line below to find the ratio of the distances. Choose the statement below that is true about the given values.

A B C D

A C E

4, 6, 14 6, 9, 21

5. Multiple Choice A D

5 x 7 x

C

3 2

3 2

The value in column A is greater. The value in column B is greater. The values are equal. The relationship cannot be determined from the given information.

A

4 2

Chapter 8

.

B

0 2

C

4

D

6

E F

8 10

2

5 2

3

11 2

Column A

6. Multiple Choice

A

Column B CD CE DF BD

Which ratio describes the simplified width to length ratio of ABCD?

7.0 in.

8.

EF AB AC BE

B

9.

2.5 in.

D

C

A D

2.5 7.0 0.5 1.4

B E

25 70 5 14

C

70 25

Copyright © McDougal Littell Inc. All rights reserved.

Geometry

Georgia Standardized Test Practice Workbook

51

LESSON

8.2

GA QCC: 1, 2

Standardized Test Practice

For use with pages 465­471

GHSGT: 4, 5, 9, 19, 36, 40

TEST TAKING STRATEGY

Do not panic if you run out of time before answering all of the questions. You can still receive a high test score without answering every question.

5. Multiple Choice A D

1. Multiple Choice

Which choice below completes the sentence to make a true statement? 3 7 "If ? ." , then x y

A D

The geometric mean of x and 5 is 15. Find the value of x. 3 5 3

B E

10 45

C

15

3 x 3 7 5 If x

y 7 x y

B E

3 7

y x

C

x 3

7 y

6. Multiple Choice

none of these

2. Multiple Choice A B C D E

Which statement is false? y 5 x y 3 , then . 3 x 3 17 8 17 x 2 If , then . x 2 10 8 10 15 17 15 y 17 x If , then . x y x y 6 7 5 n 6 5 If , then . 7 n 7 n 12 7 9 x If , then . 7 12 x 9 In the diagram, AB BD AC . CE

There are 36 students in a gym class. If 1 of the students are freshmen 4 and 2 of the remaining students are seniors, 3 how many seniors are in the class? 6 18

B E

A D

12 24

C

15

7. Multiple Choice

The points 3, 1 , 3, 3 , and x, 5 are collinear. Find the value of x by setting up and solving a proportion. 1 5

B E

A D

2 4

C

9

8. Multiple Choice

3. Multiple Choice

A model truck is 13.5 inches long and 7.5 inches wide. The original truck was 12 feet long. How wide was it? 62 ft 3 8.4 ft

B E

A D

Find the length of AE.

Chapter 8

A B C D E

7.5 ft 21.6 ft

C

54 ft 5

7.5 15 17.5 131 3 1 283

E

D

6

Quantitative Comparison

B

8

In Exercises 9 and 10, choose the statement below that is true about the given value.

A B C D

C

10

A

4. Multiple Choice

In the diagram,

UV UZ

WX . WY

The value in column A is greater. The value in column B is greater. The two values are equal. The relationship cannot be determined from the given information. Column A Column B The geometric mean of 7 and 19 The geometric mean of 6 and 10

Find the length of WX.

A B C D E

52

21 3

U 2 3.5 V 10.5 3

W X

7

9.

The geometric mean of 8 and 16 The geometric mean of 5 and 12

42 3 112 3

Z

Y

10.

Geometry

Georgia Standardized Test Practice Workbook

Copyright © McDougal Littell Inc. All rights reserved.

LESSON

8.3

GA QCC: 20, 21, 23

Standardized Test Practice

For use with pages 473­479

GHSGT: 22, 23, 24, 40

TEST TAKING STRATEGY

1. Multiple Choice

Always look for shortcuts that will allow you to work through a problem more quickly.

5. Multiple Choice

Heptagons ABCDEF and MNOPQR are similar. Which statement of proportionality is not true?

A F E D B C R Q P M N

ABCD ~ EFGH. The perimeter of ABCD is 18. What is the length of BC?

E A B C H

6 15 8

F

7

O D G

A

4 3.5

B E

3 7

C

7.5

A C E

BC NO RM AF BC NO

ED QP CD OP FA RM

B D

RQ FE MN AB

OP CD DE PQ

D

6. Multiple Choice

The ratio of one side of ABCD to the corresponding side of EFGH is 1.5 to 4. The perimeter of EFGH is 38 inches. Find the perimeter of ABCD. 14.25 in. 1011 in. 3

B E

A D

28.5 in. 502 in. 3

C

61 in. 3

2. Multiple Choice A B C D

The two trapezoids shown are similar. What are the values of x and y? x y x y x y x 40, 10 55, 5 2y 55, 10 110, y

2x 15

Quantitative Comparison

In Exercises 7 and 8, use the diagram to choose the statement that is true given that ABCDE ~ LMNOP.

70

8

12

5

E

x

110, y

10

A B C D

3. Multiple Choice A B C D E

Find the scale factor of MNOP to QRST, given that MNOP ~ QRST. 1:5 3:5 2:5 5:2 5:3

Q 2 T R

6

The value in column A is greater. The value in column B is greater. The two values are equal. The relationship cannot be determined from the given information.

L A z B

9

Chapter 8

M x N

M

5

10

N

2z

6

P

C y

13.5 8

S O

E

D

P

12

O

Column A

7. 8.

Column B y

4. Multiple Choice

The ratio of the perimeters of ABC to KLM is 3:5. Which ratio could not be a ratio of two corresponding sides? 1.5 2.5 3:5

B E

x AE AB

LP

A D

6 10 6:15

C

9:15

Copyright © McDougal Littell Inc. All rights reserved.

Geometry

Georgia Standardized Test Practice Workbook

53

LESSON

8.4

GA QCC: 20, 21, 23

Standardized Test Practice

For use with pages 480­487

GHSGT: 22, 23, 24, 40

TEST TAKING STRATEGY

When checking your work, try to use a method other than the one you originally used to get your answer. If you use the same method, you may make the same mistake twice.

4. Multiple Choice

1. Multiple Choice

The triangles below are similar. Which choice below is the correct statement of proportionality?

A D

ABC ~

A

5

DBE. Find the

values of x and y.

A B C D

x y x y x x y x

6, 10 131, 2 10 6, y

1 132,

D

9

5

C

10 3

x

4

y

B

C

E

F

5 6, y

E

12

B

A C E

AB DE AC DE EF BC

AC DF AB DF DE AC

BC EF CB EF AB DF

B D

DF BC AB DF

AB DE AC DE

EF AC EF BC

E

5. Multiple Choice

What is the perimeter of

A

4 3

trapezoid BCDE?

A B C D E

26 28 31 38

D

6 14

E

B

2. Multiple Choice

to

A B C

Which angle is congruent M in the similar triangles below? N Q QOP P

O N Q

C

30 or 30.1

6. Multi-Step Problem

Use the diagram to

Chapter 8

answer parts (a)­(e).

C P

D E

cannot be determined

M D B

4 6

3. Multiple Choice

The triangles are similar. Which of the following is not a correct statement? K

A F

5

F

8

E

a. Find the length of BC. b. Find the length of BF.

E G M L

c. What is the scale factor of d. Find the perimeter of e. Critical Thinking

ABF to

ACE?

A C E

54

K GE ML M

F GF MK G

B D

FEG ~ KLM ML KL FG FE

BCDF.

show that

ABF ~

Explain how you could FDE.

Geometry

Georgia Standardized Test Practice Workbook

Copyright © McDougal Littell Inc. All rights reserved.

LESSON

8.5

GA QCC: 6, 20, 21, 23

Standardized Test Practice

For use with pages 488­496

GHSGT: 22, 23, 24, 40

TEST TAKING STRATEGY

Sketch graphs or figures in your test booklet to help you solve the problems. Even though you must keep your answer sheet neat, you can make any kind of mark you want in your test booklet.

C D E

E

1. Multiple Choice

B

10 4

Use the diagram below to determine which statement(s) are true.

ABD ~ ABD ~ ABD ~

DEC by SSS Similarity Thm. ECD by AA Similarity Post. DEC by AA Similarity Post.

A

8

C D

15 12

6

4. Multiple Choice

H

8

F

6 3

Which similarity statement and postulate or theorem correctly identifies the triangles' relationship?

A

6

G

I

D

12

I. II. III.

A D

ABC ~ ABC ~ DEF ~ I I and III

DEF GHI GHI

B E

C

9

II

C

III

B

8

E

none of these

A B C D

ABD ~ ABC ~ ABC ~ ABC ~ ABC ~

CDE by SSS Similarity Thm. CDE by SAS Similarity Thm. EDC by SSS Similarity Thm. EDC by AA Similarity Post. EDC by SAS Similarity Thm. Find the distance labeled x

Chapter 8

2. Multiple Choice

What is the scale factor for the triangles below?

15

20 9 22 12

E

5. Multiple Choice

13.2

in the diagram.

C

3 5

A D

3 2 2 5

B E

4 3 3 4

A B C D E

32.5 ft 42.5 ft 35 ft 48.2 ft 43.5 ft Solve for x.

B

10 10 ft 26 ft 8 ft

x

3. Multiple Choice

Which similarity statement and postulate or theorem correctly identifies the triangles' relationship?

B C

6. Multiple Choice A B C

18.75 17.2 18 19 12.5

C

12

A

15

x

A

E

D

D E

D

22.5

A B

ABD ~ ABD ~

ECD by SSS Similarity Thm. ECD by SAS Similarity Thm.

Copyright © McDougal Littell Inc. All rights reserved.

Geometry

Georgia Standardized Test Practice Workbook

55

LESSON

8.6

GA QCC: 1, 15, 20, 21, 22

Standardized Test Practice

For use with pages 498­505

GHSGT: 4, 36

TEST TAKING STRATEGY

It is important to remember that your SAT score will not solely determine your acceptance into a college or university. Do not put added pressure on yourself to do well. If you are not satisfied with your SAT score, remember that you can take it again.

5. Multiple Choice A B C D

O

8

1. Multiple Choice A B C D E

What is the length of OP?

M

Find the value of y.

1.5 102 3 5 6 73

1

16 36 8 40 54 62

12

4

y

24

Q 3 P N

E

2. Multiple Choice

Which value of AB would

make EB DC?

A B C D E

Quantitative Comparison

A

51

4 8 18 28 36

D

17

In Exercises 6­8, use the diagram below to solve for the indicated values. Choose the statement that is true about the given values.

A B C D

E

B 12 C

3. Multiple Choice A B

Find the value of x.

A

The value in column A is greater. The value in column B is greater. The two values are equal. The relationship cannot be determined from the given information.

8

22 24 26 28 30

42 15 20

B C

24 7 10.5 F G

Chapter 8

C D E

x

E

D H

Column A

4. Multiple Choice A B C D E

Column B GH EG FH

Find the value of x.

8 18

102 3 6 22 36 54

24

6. 7. 8.

BC BD AB CD

x

56

Geometry

Georgia Standardized Test Practice Workbook

Copyright © McDougal Littell Inc. All rights reserved.

LESSON

8.7

GA QCC: 1, 15, 20, 21, 39, 40, 41

Standardized Test Practice

For use with pages 506­513

GHSGT: 2, 4, 22, 23, 40

TEST TAKING STRATEGY

Avoid spending too much time on one question. Skip questions that are too difficult for you, and spend no more than a few minutes on each question.

4. Multiple Choice A

3 2 2

1. Multiple Choice

Which statements below

Find the values of x and y.

C' C y A A' x

2 4

are true? I. A dilation with a scale factor of is an enlargement, 150% bigger. II. A dilation with a scale factor of 3 is an enlargement, 66% bigger. III. A dilation with scale factor k is a reduction if 1 < k < 1.

A D

x y x y x y x x

2 3,

8 6, 8 6, 12 6, y 24, y 4 4

B

24

B C D E

B'

12

I I and II

B E

II II and III

C

III

5. Multiple Choice 2. Multiple Choice

Which choice below correctly identifies the dilation and scale factor?

P'

3

The dilation has center E. Find the values of x and y.

A

15

B x B'

10 20

5 2

A' y

7

P

E

15 30

D'

C' C

A B C D E

reduction; k reduction; k enlargement; k enlargement; k enlargement; k

2 5 3 5 2 5 3 5 5 2

D

A C E

x x x

7.5, y 6, y 6, y

21 B 3.5 14

D

x x

10, y 7.5, y

15 14

Chapter 8

6. Multi-Step Problem a. On a coordinate plane, draw b. Draw a dilation of

3. Multiple Choice

Which choice below correctly identifies the dilation and scale factor?

C P' 36 P

12

ABC with vertices A 1, 5 , B 3, 6 , and C 3, 3 . ABC. Use the origin as center and a scale factor of 2 to draw ABC. ABC. Use the origin as center and a scale factor of 1 to draw 2 ABC.

c. Find the length of B C . d. Draw a dilation of

A B C D E

reduction; k reduction; k reduction; k enlargement; k enlargement; k

14 36 36 12 12 36 36 12 12 36

e. Find the length of A C . f. What scale factor could you use to go from

A B C to

ABC ?

Copyright © McDougal Littell Inc. All rights reserved.

Geometry

Georgia Standardized Test Practice Workbook

57

LESSON

9.1

GA QCC: 1, 20, 21, 23

Standardized Test Practice

For use with pages 527­534

GHSGT: 4, 22, 23, 24

TEST TAKING STRATEGY

1. Multiple Choice

Read each test question carefully. Always look for shortcuts that will allow you to work through a problem more quickly.

C

5. Multiple Choice A

B D

Use the diagram at the right to choose the correct similarity statement for the three triangles. A

A B C D E

Find the value of y. Round to the nearest hundredth. 3.20 2.55 1.32

B D

5.29 4.45

7

4

C E

y

ABC ~ ABC ~ ABC ~ ABC ~ ABC ~

CDB ~ CBD ~ CBD ~ CDB ~ BCD ~

ACD ADC ACD ADC ADC

6. Multiple Choice A B C

Find the value of x. Round to the nearest hundredth. 10.2 3.08 8.06 5 8.13

x

8 5

2. Multiple Choice

Use the diagram in Exercise 1 to choose the proportion that is false. AB CB AB AC CB DB AC AD

B D

D E

A C E

BD CD BD CB

CD AD CD AB

7. Multiple Choice

Find the value of z. Round to the nearest hundredth. 42.68 64.29 62.30

B D

z

14 30

A C E

20.49 56.28

none of these

3. Multiple Choice

Use the diagram below to identify the similar triangles and complete the proportion. A CA BA BA ?

A C E

8. Multi-Step Problem

AC DC DA

B D

BD BC

B

D

You want to hang a tire swing from a tree in your backyard. The branch is horizontal to the ground. The diagram shows the vertical distance from your eye to the ground, and from you to the swing.

T

a. What is HG?

C

b. What is TG? c. If the tire swing is to

4. Multiple Choice

Chapter 9

Use the diagram below to find the value of h. Round to the nearest hundredth, if necessary. 9.60 8.70 9.25

B D

A C E

9.50 10.23

16

h

20

12

hang 21 feet from the 2 ground, and the tire H 8.2 ft A has a diameter of 3 5.4 ft feet, approximately G how much rope is needed to hang the swing? triangles.

d. Write a similarity statement for the three

58

Geometry

Georgia Standardized Test Practice Workbook

Copyright © McDougal Littell Inc. All rights reserved.

LESSON

9.2

GA QCC: 1, 24

Standardized Test Practice

For use with pages 535­541

GHSGT: 4, 32, 35

TEST TAKING STRATEGY

When checking your work, try to use a method other than the one you originally used to get your answer. If you use the same method, you may make the same mistake twice.

6. Multiple Choice A

c a C B

1. Multiple Choice

Which equations below are

true about I. a II. c III. b

A D

ABC? c2 a

2

Find the area of the figure. Round to the nearest tenth, if necessary. 307.5 m2 410 m

2

b2 b a

B E

2

39 m 36 m 5m

B C D

c

A

585 m2 615 m2 1230 m2

b

I I and II

II all of these

C

III

E

7. Multiple Choice 2. Multiple Choice A B C D E

Find the value of x. Round to the nearest tenth, if necessary. 25 in. 26.4 in. 14 in. 13.6 in. 14.2 in.

8.

x

21 in. 16 in.

Find the area of the figure. Round to the nearest hundredth, if necessary. 79.5 m2 53.61 75 m2 57.0 m2 40.74 m2

18 m 12 m 8m

A B C D E

m2

Quantitative Comparison

3. Multiple Choice A B C D E

Find the value of y. Round to the nearest hundredth, if necessary. 10.25 cm 15.26 cm 25 cm 21 cm 14.28 cm

8 cm

Use the diagram below to find the variables. Choose the statement below that is true about the given number. The value of column A is greater. The value of column B is greater. The two values are equal. The relationship cannot be determined from the given information.

y

y

13 cm

A B C D

4. Multiple Choice

Find

10

the value of x.

A C E

5 5 2 7.5

B D

2 5 7

10

x

15

x

Chapter 9

5. Multiple Choice

Find the

B

Column A x

26 ft

Column B y

area of the figure.

A C E

260 ft2 240 ft2 140 ft2

130 ft2 120 ft2

D

10 ft Geometry

Georgia Standardized Test Practice Workbook

Copyright © McDougal Littell Inc. All rights reserved.

59

LESSON

9.3

GA QCC: 1, 24

Standardized Test Practice

For use with pages 543­549

GHSGT: 4, 32, 35

TEST TAKING STRATEGY

Avoid spending too much time on one question. Skip questions that are too difficult for you, and spend no more than a few minutes on each question.

6. Multiple Choice

1. Multiple Choice

Let the numbers represent the lengths of the sides of a triangle. Which of the triangles are right triangles? I. 4, 5, 6 II. 15, 20, 25 IV. 5, 13, 14

B E

Find the value of y that makes the triangle an acute triangle.

A

26

18

III. 15, 36, 39

A D

20 18 16

B D

18.5 17

y

I III and IV

II II and IV

C

II and III

C E

2. Multiple Choice

If two sides of a triangle are 8 and 10, what measurement could represent the third side if the triangle is a right triangle? 12 A or B

B E

7. Multiple Choice

Given points P 2, 4 and Q 2, 6 are two vertices in a right triangle, which point could represent the third vertex?

A D

A D

2 41 B or C

C

6

0, 9 B and C

B E

4, 2

C

0, 0

none of these

3. Multiple Choice

Let the numbers represent the lengths of the sides of a triangle. Which of the triangles are acute triangles? I. 10, 24, 26 II. 6, 8, 9.5 IV. 45, 60, 75

B E

Quantitative Comparison

In Exercises 8 and 9, choose the statement below that is true about the given value.

A B C D

B

III. 12, 17, 22

A D

I and II III

II III and IV

C

II and III

The value in column A is greater. The value in column B is greater. The values are equal. The relationship cannot be determined from the given information.

F

4. Multiple Choice

Which set of numbers can represent the side lengths of an obtuse triangle? 1, 2, 3 3, 7, 7.5 none of these

8. 9.

12

y

x

y

w

A C E

B D

3, 5,

34

A z C E z G

12, 15, 3 41

5. Multiple Choice

Find the value of x that makes the triangle a right triangle. 12 13 15 17 20

9

Column A x x

Column B w when w when EFG is acute EFG is obtuse

Chapter 9

A B C D E

x

60

Geometry

Georgia Standardized Test Practice Workbook

Copyright © McDougal Littell Inc. All rights reserved.

LESSON

9.4

GA QCC: 1, 24, 25

Standardized Test Practice

For use with pages 551­557

GHSGT: 4

TEST TAKING STRATEGY

Staying physically relaxed during the SAT is very important. If you find yourself tensing up, put your pencil down and take a couple of deep breaths. This will help you stay calm.

5. Multiple Choice A

y

1. Multiple Choice A B C D E

Find the values of x and y. 6 2 4 3 6 6

x

Find the value of x. 10 2 5

10

x x x x x

6, y

6 3

3 2, y 2 3, y 6, y 6 2, y

5 2 2 5 2 10 2

B D

x

C

45

6 2

E

2. Multiple Choice A B C D E

Find the values of a and b. 9 2 9 3 18 6 3 3 3 Find the values of x and y. 3 3 2 2 3

3

6. Multiple Choice

a a a a a

9, b 18, b

b

60 9

Find the area of the figure. Round to the nearest tenth if necessary. 68.2 m2 70.1 m2 187.0 m2

B D

30 18 m

9 3, b 3 3, b 6 3, b

A

a

93.5 m2 140.3 m2

C E

3. Multiple Choice A B C D E

7. Multiple Choice

x x x x x

3 2, y 3, y 2, y 3 2, y 2, y

y

The perimeter of a square is 54 cm. Find the length of a diagonal, rounding to the nearest tenth. 10.4 cm 22.4 cm

B E

3 2

x

A D

19.1 cm 38.2 cm

C

13.5 cm

8. Multiple Choice

45

4. Multiple Choice A B C D E

Find the values of m and n. 8 3 3 16 3 3 16 16

8

The side of an equilateral triangle is 12 cm. Find the length of an altitude of the triangle. 6 3 cm 12 3 cm

B E

m m m m m

16 3 ,n 3 16, n 8 3 ,n 3 16 3, n 8 3, n

A D

6 2 cm C 12 2 cm

6 cm

8 3

n m

30

9. Multi-Step Problem

ABC is equilateral

B

and DEGF is a square.

a. Find DG. b. Find DI. c. Find DJ. d. Find DB. e. Find BJ. f. Find the area of

A

5

D

J I H

45

E

Chapter 9

F

G

C

trapezoid ADEG. Round to the nearest tenth.

Copyright © McDougal Littell Inc. All rights reserved.

Geometry

Georgia Standardized Test Practice Workbook

61

LESSON

9.5

GA QCC: 1, 26, 27

Standardized Test Practice

For use with pages 558­566

GHSGT: 4, 35

TEST TAKING STRATEGY

If you find yourself spending too much time on one test question and getting frustrated, move on to the next question. You can revisit a difficult problem later with a fresh perspective.

6. Multiple Choice A

B c

1. Multiple Choice

Use the triangle below. Choose the correct ratio to find tan B. b a a c b c A.

B D B D

Find the perimeter of the triangle. Round to the nearest tenth. 42.2 in. 39.9 in. 37.2 in. 39.1 in. 33.1 in.

10 in. 37

A C E

a b b c

A

B C D

a C

b C

E

2. Multiple Choice

Find the 0.4167 1.0833

7. Multiple Choice A

24 26

sine of

A C E

Find the area of the triangle. Round to the nearest tenth. 93.5 cm2 62.4 cm2 54 cm2 140.3 cm2 81 cm2

12 cm 30 18 cm

0.3846 0.9231 2.4

B C

B

10

A

D E

3. Multiple Choice A B C D E

Find the cosine of

C

5 10

B.

B

1.7321 0.8660 2 1.1547 0.5774

Quantitative Comparison

5 3

In Exercises 8 and 9, choose the statement below that is true about the given value.

A B C D

A

4. Multiple Choice A D

Use the diagram in Exercise 3 to find the tangent of B. 1.7321 1.1547

B E

The value in column A is greater. The value in column B is greater. The two values are equal. The relationship cannot be determined from the given information.

B

0.8660 0.5774

C

2

5. Multiple Choice

Find the value of x.

A x

35

35

40

Chapter 9

A B C D E

62

16 sin 35 16 cos 35 sin 35 16 16 sin 35 16 tan 35

Geometry

Georgia Standardized Test Practice Workbook

D

15

C

Column A

16

Column B BC

8. 9.

AD BD AB AD

BC

Copyright © McDougal Littell Inc. All rights reserved.

LESSON

9.6

GA QCC: 26, 27

Standardized Test Practice

For use with pages 567­572

TEST TAKING STRATEGY

The mathematical portion of the SAT is based on material taught in your high school mathematics courses. One of the best ways to prepare for the SAT is to keep up with your regular studies and do your homework.

6. Multiple Choice

1. Multiple Choice

Which statements below

are true? I. You can solve a right triangle if you are given the lengths of two sides. II. You can solve a right triangle if you are given the measure of the two acute angles. III. You can solve a right triangle if you are given only one side and one acute angle.

A D

In the diagram below, what are the measures of AB and CB, rounded to the nearest tenth? AB AB AB AB AB 46.9, CB 24.9, CB 46.9, CB 24.9, CB 41.4, CB 41.4 46.9 24.9 41.4 46.9

C

22

A B C D E

B

28

I I and III

B E

II

C

III

A

all of these

Quantitative Comparison

2. Multiple Choice

measure of acute

A D

Which is the approximate A when tan A 0.698?

B E

In Exercises 7­9, use the diagram below to find the values. Choose the statement below which is true about the given value.

A B C D

A

44.3 45.7

12.2 35.2

C

34.9

3. Multiple Choice

is the measure of tenth?

A B C D E

In the diagram below, what M, rounded to the nearest

M

The value in column A is greater. The value in column B is greater. The two values are equal. The relationship cannot be determined from the given information.

63.6 63.4 N 26.6 26.4 63.5

3

B

15 6 31

E O

D 5 C

4. Multiple Choice

the measure of

A B C D E

In the diagram below, find Z. Round to the nearest tenth.

Column A

7. 8.

Column B AB BC

AD DB ED BC AD

48.6 28.1 61.9 41.4 29.6

X

17

9.

BC

Chapter 9

Y

15

Z

5. Multiple Choice A D

In the diagram in Exercise 4, find the measure of XY. 6 9

B E

10 8

C

7

Geometry

Georgia Standardized Test Practice Workbook

Copyright © McDougal Littell Inc. All rights reserved.

63

LESSON

9.7

GA QCC: 46

Standardized Test Practice

For use with pages 573­580

GHSGT: 3

TEST TAKING STRATEGY

1. Multiple Choice

\

Make sure that you are familiar with the directions before taking a standardized test.

\

Points M 7, 1 and N 2, 8 are the initial and terminal points of vector MN . Which choice below is the component form of MN ?

\

6. Multiple Choice

\

7, 2 and Let P 5, 8 . What is the component form Q and magnitude of P Q , rounded to the nearest tenth?

\ \

A D

5, 7 5, 7

B E

12.7 9, 7

C

9,

9

A C E

2, 6 , 6.3 12, 10 , 15.6 12, 10 , 15.6

B D

2,

6 , 6.3 2, 6 , 6.3

2. Multiple Choice

\

Points Q 4, 1 and R 12, 4 are the initial and terminal points of vector QR . What is the magnitude of vector QR ?

\

\

7. Multiple Choice

\

A D

8.5 16.8

B E

8, 3 16, 5

C

8,

3

x, 4 and Let A 14, y . If A B B 12, 6 , what are the values of x and y?

\ \

A C E

x x x

2, y 2, y 2, y

10 10 10

B D

x x

2, y 2, y

2 2

3. Multiple Choice

\

Points A 3, 2 and B 6, 8 are the initial and terminal points of vector BA . What is its magnitude?

A D

\

3, 10 10.6

B E

9, 10.8

6

C

10.4

8. Multiple Choice

5, 9 . Vector XY Which vector below has the same magnitude but a different direction? 3, 2 4, 10

B E

4. Multiple Choice A B C D E

Use the diagram below to find the magnitude and direction of EF .

\

A D

4, 10 5, 9

C

10, 18

11.3, 69.3 17.9, 12.9 17.9, 77.1 8.94, 26.5 8.94, 63.5

2

y

F

9. Multi-Step Problem

E

2 x

A jet is flying from Cleveland to New York. A smaller plane takes off from the same airport and heads towards Detroit. They both encounter a strong wind blowing from the west at 80 miles per hour, 80, 0 . represented by w

\ \

a. The jet's velocity vector is represented by

\

5. Multiple Choice

\

K

A C

5, Let J 15, 3 . What is J K ?

\ \

1 and

450, 510 . What is its speed and j direction if there were no wind?

b. The plane's velocity vector is represented

\

10, 4 10, 20, 4 4

B D

20, 2 10, 2

Chapter 9

E

by p 300, 200 . What is its speed and direction if there were no wind? c. What is the jet's speed and direction after encountering the wind described by w ?

\

d. What is the plane's speed and direction

after encountering the wind described by w?

\

64

Geometry

Georgia Standardized Test Practice Workbook

Copyright © McDougal Littell Inc. All rights reserved.

LESSON

10.1

GA QCC: 28, 29

Standardized Test Practice

For use with pages 595­602

GHSGT: 29

Chapter 10

TEST TAKING STRATEGY

Sketch graphs or figures in your test booklet to help you solve the problems. Even though you must keep your answer sheet neat, you can make any kind of mark you want in your test booklet.

5. Multiple Choice A secant. C

For Exercises 1­5, use the diagram below.

A C

HJ is best described as a B chord.

D

B

common external tangent. diameter.

common internal tangent.

E

D F I H G L J K E

6. Multiple Choice

What is the diameter of

5 3 2

C?

A C E

8 3 5

B D

4 2

C

1. Multiple Choice A C E

FB is best described as a

B D

radius. chord. tangent.

diameter. secant.

7. Multiple Choice A C

How many common tangents do the circles have? 0 2 4

B D

1 3

2. Multiple Choice A C D E

AJ is best described as a

B

E

diameter. chord.

secant.

8. Multi-Step Problem

y

common external tangent. common internal tangent. CD is best described as a

B

Use the diagram below to answer parts (a)­(d).

3. Multiple Choice A C D E

diameter. chord.

secant.

2

A

common external tangent. common internal tangent. CG is best described as a

B D

B

1 x

4. Multiple Choice A C E

diameter. secant. chord.

radius. tangent.

a. What is the center and radius of b. What is the center and radius of

A? B?

c. What is the intersection of the circles? d. Describe the common tangents to the cir-

cles. Are they internal, external, or both?

Copyright © McDougal Littell Inc. All rights reserved.

Geometry

Georgia Standardized Test Practice Workbook

65

LESSON

Chapter 10

10.2

GA QCC: 28, 29

Standardized Test Practice

For use with pages 603­611

GHSGT: 29

TEST TAKING STRATEGY

Do not panic if you run out of time before answering all of the questions. You can still receive a high test score without answering every question.

A B C

55

For Exercises 1­4, use the circle at the right.

6. Multiple Choice A D

What is m EDB in

B E

Exercise 5? 100 330

150 340

C

300

E D

7. Multiple Choice

Use the diagram to find the value of x. Round to the nearest hundredth, if necessary. 4 5.62 5.83

B D

A 1. Multiple Choice A D

5 6.31

6

5 3

Find mBC .

B E

C C

55 110

90 125

35

E

x

2. Multiple Choice A D

Find mCD .

B E

8. Multiple Choice

Use the diagram below to

x

10 22

find the value of x.

C

55 110

90 125

35

A C E

10 22 44

B D

20 11

3. Multiple Choice A D

Find m CAE .

B E

180 215

125 300

C

145 Quantitative Comparison In Exercises 9 and 10, use the diagram that is true.

A B

4. Multiple Choice

Which statement is not

B

The value in column A is greater. The value in column B is greater. The two values are equal. The relationship cannot be determined from the given information.

A

true?

A C D

m AC m AE m CD

m CD m BC m AE

m AB m AD

m ED m EB

C D

m CD

E

5. Multiple Choice A C E

Find the value of x.

A x Ex B D

20 45 60

B D

30 50

E G

C

5x

C D

F

B

9. 10.

66 Geometry

Georgia Standardized Test Practice Workbook

Column A m DGE m ABC

Column B m DAE m CAB

Copyright © McDougal Littell Inc. All rights reserved.

LESSON

10.3

GA QCC: 2, 28, 29

Standardized Test Practice

For use with pages 613­620

GHSGT: 29

Chapter 10

TEST TAKING STRATEGY

If you find yourself spending too much time on one test question and getting frustrated, move on to the next question. You can revisit a difficult problem later with a fresh perspective.

A B

1. Multiple Choice

6. Multiple Choice A C

Find the value of x.

(12x 10)

What is m AB?

A C E

5 8 7.5

B D

3 10

(7x

10 30 60

B D

20 40

20

E

5)

C

2. Multiple Choice

If an inscribed angle has a 100 , what is the measure of the measure of intercepted arc? 100 0

B E

7. Multiple Choice A B C D E

Find the values of x and y. 75 100 80 105 115 Find the values of x and y. 84 48 42 84 42

A

84 80 75

x x x x x

80, y 105, y 75, y 100, y 90, y

x

y

A D

200 180

C

50

3. Multiple Choice A C E

Find the value of x.

A

178

178 B 89 91

D

356 182

8. Multiple Choice A

x B

x x x x x

6, y 42, y 42, y 90, y 48, y

B y

B C

C

D E

x D

84

C

4. Multiple Choice

If m LNM

M

280 , find the

L

value of y.

A C E

40 280

B

80 140

y N

Quantitative Comparison In Exercises 9 and 10, use the diagram to choose the statement below that is true.

A B C D

160 D

The value in column A is greater. The value in column B is greater. The two values are equal. The relationship cannot be determined from the given information. Column B m ED y

E

100 4x 5y

5. Multiple Choice A B C D E

Find the values of a and b. 50 50 25 25 25

b

25

a a a a a

50, b 25, b 50, b 25, b 100, b

a

Column A

9. 10.

m AB x

D x C

A

4x

B

Copyright © McDougal Littell Inc. All rights reserved.

Geometry

Georgia Standardized Test Practice Workbook

67

LESSON

Chapter 10

10.4

GA QCC: 28, 29

Standardized Test Practice

For use with pages 621­627

GHSGT: 29, 31

TEST TAKING STRATEGY

The mathematical portion of the SAT is based on material taught in your high school mathematics courses. One of the best ways to prepare for the SAT is to keep up with your regular studies and do your homework.

6. Multiple Choice

1

1. Multiple Choice

Find m 1.

A C E

Find m 1.

170

150

170 190 340

B D

85 95

A C E

75 95 40

B D

190 150

1 40

7. Multiple Choice 2. Multiple Choice

Find m AB.

A C E

A

Find m 1.

A

86

64 108 86

B D

32 54

1 22

110 140 35

B D

70 220

C

70

C E

B

8. Multiple Choice A

Find the value of y.

y

26 77 102 51 52

(9x 3)

3. Multiple Choice

A

58

Find m ABC.

A C E

B C D

B

58 122 244

B D

116 29

C

(5x

1)

E

4. Multiple Choice

If m EGF

F

6x

12 ,

find the value of x.

A C E

Quantitative Comparison In Exercises 9 and 10, choose the statement that is true.

A B

22 16 20

B D

11 10

G

72

C

E

D

The value in column A is greater. The value in column B is greater. The two values are equal. The relationship cannot be determined from the given information.

A

(5x 9)

5. Multiple Choice

If m LNM

N

8x

12 ,

E M x F

(2x 12)

find the value of x.

A C E

14 28 34.8

B D

16.8 29

2x

D

C

B 56

L

Column A

9. 10.

Column B m AC m AE

Copyright © McDougal Littell Inc. All rights reserved.

m EAB m CD

68

Geometry

Georgia Standardized Test Practice Workbook

LESSON

10.5

GA QCC: 1, 28, 29, 46

Standardized Test Practice

For use with pages 629­635

GHSGT: 4, 29, 31

Chapter 10

TEST TAKING STRATEGY

Make sure that you are familiar with the directions before taking a standardized test. This way, you do not need to worry about the directions during the test.

4

1. Multiple Choice

6. Multiple Choice

8

Find the value of x.

A C E

3 5 8

B D

4 6

x

6

You are standing 16 feet from a circular swimming pool. The distance from you to a point of tangency is 25 feet. What is the approximate diameter of the pool? 23 ft 38 ft

B E

A D

8 5y 3 2

46 ft 15 ft

C

19 ft

2. Multiple Choice

Find the value of y.

A C E

7. Multiple Choice A B C

2 4 6

B D

3 5

Find the values of x and y. Round to the nearest tenth, if necessary. x x x x x 14.4, y 12, y 14.4, y 12, y 24, y 8 8 8 18

y

y

18

x

8 12

3. Multiple Choice

9 6

Find the value of x.

A C E

8 12

D E

10 9.6 14

B D

5 12

x

10

4. Multiple Choice

Find the value of y.

A C E

8 5

3.2 4.9 1.8

B D

12.8 7.8

x

Quantitative Comparison In Exercises 8 and 9, use the diagram to choose the statement below that is true. A The value in column A is greater. B The value in column B is greater. C The two values are equal. D The relationship cannot be determined from the given information.

A z D 18 x G 22 E 6 y H C B

5. Multiple Choice A C E

Find the value of x. Round to the nearest tenth, if necessary. 22 5.3 14

x

B D

8.8 6.6

7 4 15 12

F

Column A

8. 9.

Column B y HB

x z

Copyright © McDougal Littell Inc. All rights reserved.

Geometry

Georgia Standardized Test Practice Workbook

69

LESSON

Chapter 10

10.6

GA QCC: 42, 46

Standardized Test Practice

For use with pages 636­640

GHSGT: 29

TEST TAKING STRATEGY

1. Multiple Choice

Work as quickly as you can through the easier sections, but avoid making careless errors on easy questions.

6. Multiple Choice

What is the standard form of the equation of a circle with center 3, 2 and radius 4? x x x x x 3 3 3 3 3

2 2 2 2 2

The center of a circle is 2, 4 and a point on the circle is 1, 4 . What is the equation of the circle? x x x x x 4 2 2 2 2

2 2 2 2 2

A B C D E

y y y y y

2 2 2 2 2

2 2 2 2 2

4 16 8 16 16

A B C D E

y y y y y

2 4 4 4 4

2 2 2 2 2

9 9 9 3 3

2. Multiple Choice

What is the center of a circle with an equation of x 52 y 1 2 36? 6, 0 5, 1 5, 1

B D

7. Multiple Choice

A diameter of a circle has endpoints of 5, 6 and 5, 2 . What is the equation of the circle? x x x x x 5 5 5 5 5

2 2 2 2 2

A C E

0, 6 5, 1

A B C D E

y y y y y

2 2 2 2 4

2 2 2 2 2

16 4 4 64 4

3. Multiple Choice

What is the radius of a circle with an equation of 2 9 2 25 x 4 y 16 9 36 ?

2 3 5 6

A D

B E

4 9 25 36

C

3 4

8. Multiple Choice

The center of a circle is 5, 3 and its radius is 4. Which point lies on the exterior of the circle? 4, 4, 1, 2 5 3

B D

4. Multiple Choice A B C D E

What is the center and radius of the circle in the diagram? 1, 4 , 2 4, 3 , 2 3, 4 , 2 4, 3 , 4 3, 4 , 4

1 1 x y

A C E

6, 0 1, 4

9. Multi-Step Problem

The center of a circle is x, 2 and its radius is 3. Assume x > 4. 4, 2 , what is the value of x?

a. If another point on the circle is

b. What is the equation of the circle in

5. Multiple Choice

What is the equation of the circle in Exercise 4? A x 42 y 32 2

B C D E

standard form?

c. Graph the equation from part (b). d. Name a point on the circle, a point in the

x x x x

3 4 3 1

2 2 2 2

y y y y

4 3 4 4

2 2 2 2

2 4 4 4

interior of the circle, and a point in the exterior of the circle.

70

Geometry

Georgia Standardized Test Practice Workbook

Copyright © McDougal Littell Inc. All rights reserved.

LESSON

10.7

GA QCC: 1, 3, 42, 46

Standardized Test Practice

For use with pages 642­648

GHSGT: 4, 29

Chapter 10

TEST TAKING STRATEGY

It is important to remember that your SAT score will not solely determine your acceptance into a college or university. Do not put added pressure on yourself to do well. If you are not satisfied with your SAT score, remember that you can take it again.

For Exercises 5­7, use the graph at the right.

5. Multiple Choice

y

1. Multiple Choice

What is the locus of all points in the coordinate plane that are equidistant from points 3, 2 and 3, 16 ? The line x 3, 9 3, 14 and 3, 18 9

B D

J

A C E

The line y The line x

9 3

2. Multiple Choice

What is the locus of all points in the coordinate plane that are equidistant from points A 1, 2 and B 3, 2 and are 5 units from B. The line x 2, 2, 2 , 2, 2 4 2

B

Find the locus of points in the coordinate plane that are equidistant from H and I.

A C E

1 1

H

I

x

The line x The line y 5, 2

9 2 9 2

B D

The line y

5

5, 2 and 0, 2

A C D E

The line y

2

3 2 , 2, 2 2

6. Multiple Choice

Find the locus of points that

are 4 units from J.

A B C D E

2, 0 , 2, 4

5, 2 and 5, 10 The circle x 1, 6 and 9, 6 The circle x The circle x 5 5

2 2

3. Multiple Choice

What is the locus of all points that are equidistant from the lines y 3x 2 and 3x 5y 50. 5 0, 6 The line y The line y 0, 6 and The lines y

3 5x 3 5x

5

2

y y y

6 6 6

2

16 8 16

2 2

A B C D E

4 6 12 and y

3 5x

7. Multiple Choice

4 3x 4 3x 4 3 8 3

Find the locus of points that are 2 units from JH.

A C E

10, 0

3 5x

y y

B D

y

3 4x

2 3

A and C

4. Multiple Choice

Point D is in the interior of ABC. What is the number of possible locus points in the interior of ABC that are equidistance from ABC and 1 inch from point D? 0 points 1 point 2 points all points on the bisector of ABC cannot be determined

A and B

8. Multi-Step Problem

A B C D E

You are given seismograph readings from three locations. · At A 4, 6 , the epicenter is 10 miles away. · At B 2, 4 , the epicenter is 6 miles away. · At C 10, 4 , the epicenter is 6 miles away.

a. Graph points A, B, and C on a coordinate

plane. b. What is the locus of A, of B, and of C? c. Find the epicenter.

Geometry

Georgia Standardized Test Practice Workbook

Copyright © McDougal Littell Inc. All rights reserved.

71

LESSON

11.1

GA QCC: 13

Standardized Test Practice

For use with pages 661­668

GHSGT: 29, 30

TEST TAKING STRATEGY

Staying physically relaxed during the SAT is very important. If you find yourself tensing up, put your pencil down and take a couple of deep breaths. This will help you stay calm.

6. Multiple Choice

1. Multiple Choice A B

What is the value of x?

85

100 140 120 150 110

95

x

120 100

What is the sum of the measures of the interior angles of a convex 16-gon? 1800 2700

B E

Chapter 11

A D

2340 2880

C

2520

C D E

7. Multiple Choice

What is the measure of an exterior angle if the regular polygon has 18 sides? 18 24

B E

2. Multiple Choice A B C D E

What is the value of y?

130 75 125 145 115

A D

20 26

C

22

50 100 130 75 40

8. Multiple Choice

y

A convex octagon has exterior angles that measure 35 , 41 , 25 , 55 , 62 , 17 , and 38 . What is the measure of the exterior angle of the eighth vertex? 267 187

B E

A 3. Multiple Choice

45 87

C

177

The measure of each interior angle of a regular polygon is 144 . How many sides does the polygon have? 8 12

B E

D

A D

9 14

C

10

Quantitative Comparison

A B C

In Exercises 9 and 10, choose the statement that is true. The value in column A is greater. The value in column B is greater. The two values are equal. The relationship cannot be determined from the given information. Column B The sum of the interior angles of a pentagon The number of sides of a regular polygon whose sum of the interior angles measures 3240

4. Multiple Choice A B C D E

Find the value of x.

2x

31.25 16.25 26.25 28.75 13.75

(4x 15) (x 10) (2x 20) 3x

D

9.

5. Multiple Choice

A convex heptagon has interior angles that measure 120 , 115 , 135 , 95 , 155 , and 125 . What is the measure of the seventh interior angle? 120 155

B E

10.

Column A The sum of the exterior angles of a 19-gon The number of sides of a regular polygon with an exterior angle measuring 20

A D

115 95

C

135

72

Geometry

Georgia Standardized Test Practice Workbook

Copyright © McDougal Littell Inc. All rights reserved.

LESSON

11.2

GA QCC: 30, 32, 37

Standardized Test Practice

For use with pages 669­675

GHSGT: 26, 27, 29, 35

TEST TAKING STRATEGY

Avoid spending too much time on one question. Skip questions that are too difficult for you, and spend no more than a few minutes on each question.

5. Multiple Choice A B

6

1. Multiple Choice

Find the area of the triangle. Round to the nearest hundredth, if necessary. 12 square units 31.18 square units 5.20 square units 10.41 square units 15.59 square units

Find the area and perimeter of a square with a diagonal of 10 inches. A A A A A 25.0 in.2, P 28.3 in.2, P 50 in.2 ,P

2

14.1 in.

Chapter 11

A B C D E

50 in. 28.3 in. 100 in. 56.6 in.

C D E

56.6 in.2, P 100 in. , P

6. Multiple Choice

2. Multiple Choice

Find the area of the inscribed regular pentagon below. Round to the nearest tenth. 422.3 square units 344.4 square units 211.1 square units 688.7 square units 452.2 square units

9.7

Find the area of the shaded region. The octagon is regular. Round to the nearest tenth, if necessary. 51.1 cm2 408.5 cm2 204.2 cm2 289.0 cm2 578.0 cm2

12 cm

A B C D E

A B C D E

Quantitative Comparison

3. Multiple Choice

Find the measure of the central angles of a regular polygon with 18 sides. 10 30

B E

In Exercises 7 and 8, use the diagrams below to choose the statement that is true.

A B C D

The value in column A is greater. The value in column B is greater. The two values are equal. The relationship cannot be determined from the given information.

Regular Polygon A Regular Polygon B

A D

20 40

C

25

4. Multiple Choice

Find the perimeter of the regular hexagon. Round to the nearest tenth, if necessary. 96 units 83.1 units 166.3 units 48 units 100.5 units

7. 8.

16

A B C D E

12

12

Column A Apothem of A Area of A

Column B Apothem of B Area of B

Copyright © McDougal Littell Inc. All rights reserved.

Geometry

Georgia Standardized Test Practice Workbook

73

LESSON

11.3

GA QCC: 30, 31, 32, 36, 37

Standardized Test Practice

For use with pages 677­682

GHSGT: 26, 27

TEST TAKING STRATEGY

When checking your work, try to use a method other than the one you originally used to get your answer. If you use the same method, you may make the same mistake twice.

6. Multiple Choice

1. Multiple Choice

Chapter 11

A heptagon has one side length of 15 inches. Another similar heptagon has a corresponding side length of 12 inches. Find the ratio of the perimeters of the smaller to the larger heptagon. 16:25 25:16

B E

A D

4:5 5:4

C

15:12

A large gazebo is shaped like a regular octagon. It has sides of length 12 feet and an area of about 696 ft2. Find the area of a similar gazebo that has a perimeter of 64 feet. Round to the nearest tenth, if necessary. 309.3 ft2 261 ft2 1566 ft2

B D

A C

130.5 ft2 116 ft2

2. Multiple Choice

What is the ratio of the area of the larger heptagon to the area of the smaller heptagon in Exercise 1? 16:25 25:16

B E

E

7. Multiple Choice

A D

4:5 5:4

C

15:12

A regular pentagon has a perimeter of 25 m and an area of 43.75 m2. Find the perimeter of a similar pentagon with an area of 175 m2. 100 m 45 m

B E

3. Multiple Choice

Find the ratio of the perimeters of the larger triangle to the smaller triangle.

A D

75 m 50 m

C

25 m

8. Multi-Step Problem

5

3

Use the diagram of the rectangular swimming pool and deck area to answer parts (a)­(e). The rectangles are similar.

90 ft 60 ft

A D

25:9 3:5

B E

9:25 9:15

C

5:3

30 ft

20 ft

4. Multiple Choice

A regular hexagon has an area of 64 cm2. Find the scale factor of this hexagon to a similar hexagon with an area of 121 cm2. 64:121 11:8

B E

a. What is the area of the pool? b. What is the area of the deck? c. What is the ratio of the area of the pool to

the area of the deck?

d. How many feet of fencing is needed to go

A D

8:11

C

121:64

None of the above

around the deck?

e. If you paid $750 for 125 feet of fencing in

5. Multiple Choice

The ratio of the lengths of two equilateral triangles is 4:9. What is the ratio of their areas? 4:9 16:81

Geometry

Georgia Standardized Test Practice Workbook

your front yard, and you are using the same fencing for the pool area, how much should it cost?

A D

74

B E

9:4 81:16

C

2:3

Copyright © McDougal Littell Inc. All rights reserved.

LESSON

11.4

GA QCC: 1, 30, 31, 32, 37

Standardized Test Practice

For use with pages 683­689

GHSGT: 2, 4, 6, 7, 26, 35

TEST TAKING STRATEGY

1. Multiple Choice

Always look for shortcuts that will allow you to work through a problem more quickly.

6. Multiple Choice

Find the circumference of a circle with a diameter of 16 in. Round to the nearest hundredth. 25.13 in. 50.26 in. 201.06 in.

B D

Find the circumference of

7.2 50

A.

A B C D E

103.68 25.92 48.9 50.4 51.84

A

A C E

50.27 in. 25.14 in.

Chapter 11

2. Multiple Choice

Find the radius of a circle with a circumference of 60 m. Round to the nearest hundredth. 9.55 m 19.10 m 9.54 m

B D

7. Multiple Choice A B C D

Find the values of x and y. 4.8 1.4 4.8 4.8 1.4

A

12

A C E

4.37 m 19.09 m

x x x x x

21, y 25, y 25, y 31, y 31, y

(3y

5)

3. Multiple Choice A B C D E

Find the circumference of the circle. Round to the nearest hundredth. 9.43 cm 9.42 cm 28.26 cm 18.85 cm 28.27 cm

3 cm

220 C (5x 15)

B

E

8. Multiple Choice

Find the perimeter of the region bounded by the circular arcs and line segments. Round to the nearest hundredth, if necessary. 114.85 77.15 102.8 46.85 66.85

3 8 3 2 12

A B C D

A

6

4. Multiple Choice A B C D E

Find the length of AB . Round to the nearest tenth. 6.5 14.2 13.1 8.3 6.6

B

E 9.

C 125

Quantitative Comparison

Consider the circumference of the two circles described below. Choose the statement that is true. The quantity in column A is greater. The quantity in column B is greater. The two quantities are equal. The relationship cannot be determined from the given information. Column B Circle with diameter 4

Geometry 75

A B C D

5. Multiple Choice A B C D E

Find the radius of Round to the nearest tenth. 24.7 49.4 12.3 53.1 26.5

75 32.3

C.

C

Column A Circle with radius 4

Copyright © McDougal Littell Inc. All rights reserved.

Georgia Standardized Test Practice Workbook

LESSON

11.5

GA QCC: 30, 31, 32, 37

Standardized Test Practice

For use with pages 691­698

GHSGT: 6, 7, 26, 27, 35

TEST TAKING STRATEGY

Do not panic if you run out of time before answering all of the questions. You can still receive a high test score without answering every question.

6. Multiple Choice A B C D E

1. Multiple Choice

Find the area of a circle with a diameter of 7 inches. Round to the nearest hundredth. 153.94 in. 43.98 in. 38.48

2 2

Find the radius of C, if the area of the shaded region is 47.5 cm2. 7 cm 7.5 cm 8 cm 8.5 cm 9 cm

85

Chapter 11

A C E

B D

11.0 in.

2

19.24 in.2

in.2

2. Multiple Choice

Find the radius of a circle with an area of 66.5 cm2. Round to the nearest tenth. 9.2 cm 2.3 cm 10.6 cm

B D

7. Multiple Choice

A C E

5.3 cm 4.6 cm

Find the area of the shaded region. The three triangles are regular. Round to the nearest tenth. 67.7 cm2 35.2 cm2 39.3 cm2 46.1 cm2 56.9 cm2

4.33 cm

A B C D E

3. Multiple Choice

Find the circumference of a circle whose area is 100 m2. Round to the nearest tenth. 45.4 m 15.9 m 31.8 m

B D

A C E

35.4 m 17.7 m

Quantitative Comparison

In Exercises 8 and 9, use the diagram below to choose the statement that is true.

A B C

4. Multiple Choice

Find the area of the sector shown in the diagram. Round to the nearest tenth. 34.5 ft2 36.1 ft2 12.0 ft2 18.1 ft

2

The value in column A is greater. The value in column B is greater. The two columns are equal. The relationship cannot be determined from the given information. Given: QB bisects

A J K

4

A B C D E

6 ft 115

D

B L 2 C

28.6 ft2

AQC.

Q

5. Multiple Choice

A birthday cake is cut into 16 equal pieces. If the cake has a diameter of 14 inches, what is the area of one piece of cake? Round to the nearest hundredth. 38.48 in.2

B D

A C E

76

19.2

in.2

5.5 in.2 9.62 in.2

Geometry

14.36 in.2

Column A The area outlined 8. by ABKJ 9. The area of the circle with radius JQ.

Column B The area outlined by JQL The area of the shaded region

Georgia Standardized Test Practice Workbook

Copyright © McDougal Littell Inc. All rights reserved.

LESSON

11.6

GA QCC: 1, 30, 31, 32, 37

Standardized Test Practice

For use with pages 699­705

GHSGT: 2, 4, 7, 10, 26

TEST TAKING STRATEGY

Sketch graphs of figures in your test booklet to help you solve the problems.

5. Multiple Choice

In Exercises 1 and 2, use the diagram below.

A

0 4 8

B

C

12

D

16

E

20

F

24

Find the probability that a point chosen at random in the circle lands in the shaded region. Round to the nearest tenth. 6.9%

Chapter 11

A B C D E 1. Multiple Choice A D

26.8% 50.0% 55.6% 27.8%

Find the probability that a point chosen at random on AE is on BD. 20% 35%

B E

65

65

25% 40%

C

30%

2. Multiple Choice

Find the probability that a point chosen at random on BE is on CD. Round to the nearest hundredth. 0.15 0.27

B E

6. Multiple Choice

Find the probability that a point chosen at random in the hexagon lands in the shaded region. Round to the nearest hundredth. 5.35% 21.36% 10.68% 38.28% 69.14%

7 5

A D

0.18 0.45

C

0.25

A B C D E 7.

3. Multiple Choice

Find the probability that a point chosen at random in the regular triangle lands in the shaded region. 25% 30% 331 % 3 40% 50%

6 3

A B C D E

Quantitative Comparison

4. Multiple Choice

Find the probability that a point chosen at random lands in the shaded region. Round to the nearest tenth, if necessary. 39.3% 60.7% 64% 36% 37.6%

4

Use the diagram of the game board below. A point randomly chosen on the circle is worth the number outside the sector. A point landing in the inner circle is worth double the outside value. Choose the statement below that is true about the given number. The value in column A is greater. The value in column B is greater. The two values are equal.

8 5 2 2 7

A B C D

A B C D E

8

The relationship 3 cannot be 6 determined from the given information. 1 Column A Probability of getting 4 points

4 3

Column B Probability of getting 3 points

Geometry 77

Copyright © McDougal Littell Inc. All rights reserved.

Georgia Standardized Test Practice Workbook

LESSON

12.1

GA QCC: 3, 30, 33

Standardized Test Practice

For use with pages 719­726

GHSGT: 20, 26

TEST TAKING STRATEGY

Work as quickly as you can through the easier sections, but avoid making careless errors on easy questions.

5. Multiple Choice

1. Multiple Choice Which of the figures shown

is not a polyhedron? I. II. III.

Use Euler's Theorem to find the number of faces when a polyhedron has 8 vertices and 12 edges. 4 10

B E

A D

6 12

6

C

8

6. Multiple Choice A C E

I only III only II and III

B D

II only I and II

Which is the best description of the cross section of the figure shown? 8 A circle

B C D

square rectangle oval

E

2. Multiple Choice

Chapter 12

The polyhedron below has how many faces F and edges E ? F F F F F 6, E 6, E 8, E 8, E 8, E 18 24 18 24 30

pentagon

A B C D E

7. Multiple Choice A B C D E

The name of the regular polyhedron shown is tetrahedron. octahedron. cube. dodecahedron. iscosahedron. Choose the state-

3. Multiple Choice A C E

The polyhedron below has how many vertices? 14 16 18 The solid below is best

B D

15 17

8. Quantitative Comparison

ment below that is true.

A B

The value in column A is greater. The value in column B is greater. The two values are equal. The relationship cannot be determined from the given information. Column B The number of vertices on a solid with 22 faces, having 16 squares and 6 triangles

4. Multiple Choice

described as a

A B C D E

C D

convex, regular polyhedron. convex, nonregular polyhedron. nonconvex, regular polyhedron. nonconvex, nonregular polyhedron. none of these

Column A The number of vertices on a solid with 15 faces, having 9 hexagons and 6 squares

78

Geometry

Georgia Standardized Test Practice Workbook

Copyright © McDougal Littell Inc. All rights reserved.

LESSON

12.2

GA QCC: 3, 30, 33, 37

Standardized Test Practice

For use with pages 728­734

GHSGT: 9, 20, 26, 35

TEST TAKING STRATEGY

Make sure that you are familiar with the directions before taking a standardized test. This way, you do not need to worry about the directions during the test.

6. Multiple Choice

1. Multiple Choice A B C D E

The best mathematical name of the solid is right prism. right rectangular prism. cube. right pentagonal prism. right hexagonal prism.

Find the surface area of the right cylinder. Round to the nearest hundredth. 8.4 in. 831.27 in.2 252 in.2 395.84 in.2 506.68 in.2 451.26 in.2

15 in.

A B C D E

2. Multiple Choice A D

How many lateral edges does the figure in Exercise 1 have? 4 15

B E

7. Multiple Choice

5 10

C

7

Use the diagram to solve for the value of x given that the surface area of the figure is 286 in.2.

Chapter 12

A B C

7m

14 in. 12 in. 6 in. 8 in. 7 in.

9 in. 5 in.

3. Multiple Choice

Find the lateral area of the

right prism shown.

A B C D E

x

105 m2 90 m2 85 m

2

3m

D E

5m

74 m2 114 m2

8m

Quantitative Comparison In Exercises 8 and 9, use the solids to choose the statement below that is true.

A B C

8 in.

4. Multiple Choice A B C D E

Find the surface area of the regular right prism. 215 in. 105 in.

2

The value in column A is greater. The value in column B is greater. The two values are equal. The relationship cannot be determined from the given information. Column A Column B

4 10 6 5 5 4

160 in.2

2

D

187.5 in.2 270 in.2

4 in.

5

5. Multiple Choice

Find the surface area of a right rectangular prism with a height of 6 inches, a length of 2 inches, and a width of 8 inches. 96 in.2 152 in.2

D B

8. 9.

Lateral area Surface area

Lateral area Surface area

A C

120 in.2

E

128 in.2

56 in.2

Geometry

Georgia Standardized Test Practice Workbook

Copyright © McDougal Littell Inc. All rights reserved.

79

LESSON

12.3

GA QCC: 3, 30, 33, 37

Standardized Test Practice

For use with pages 735­742

GHSGT: 9, 20, 26, 35

TEST TAKING STRATEGY

If you are not satisfied with your SAT score, remember that you can take it again.

5. Multiple Choice A

For Exercises 1­3, use the diagram below.

Find the surface area of the cone. Round to the nearest tenth. 317.0 m2 241.7 m2 239.4 m2 278.2 m2 452.4 m2

9m 6m

6 cm

B C

5 cm 5 cm

D E

1. Multiple Choice

Find the slant height of the

6. Multiple Choice B D

pyramid.

A C

4.5 cm 6.5 cm 7.8 cm

5.5 cm 6 cm

Use the diagram to solve for x and y when the surface area is 138.23 m2. x x x x x 9.8 m, y 11 m, y 8 m, y 10.8 m, y 20 m, y 10 m 10.8 m 7.7 m 10.6 m 19.9 m

2m

A B C

Chapter 12

E

2. Multiple Choice

Find the lateral area of the

B D

y

x

pyramid.

A C E

D E

57.5 cm2 32.5 cm2 90 cm2

65 cm2 78 cm2

7. Multiple Choice

3. Multiple Choice

Find the surface area of

B D

Find the surface area of the solid. The cylinder and cones are right. Round to the nearest tenth. 8m 716.3 m2 867.1 m2 1168.7 m2 1055.6 m2 942.5 m2

15 m 6m

the pyramid.

A C E

A

2

57.5 cm 90 cm2

65 cm

2

B C D E

32.5 cm2

78 cm2

4. Multiple Choice A C E

Find the slant height of the cone. Round to the nearest tenth. 20.0 B 8.9 7.1

12

6m 8m

10.6 14.4

8. Multi-Step Problem

D

A regular pyramid has a triangular base with a base edge of 6 inches, a height of 10 inches, and a slant height of 10.33 inches.

a. Sketch the solid. b. Find the lateral area.

16

c. Find the surface area. d. Double the lengths of the base edge,

height, and slant height. What is the ratio of the surface area of the smaller pyramid to the larger pyramid?

80 Geometry

Georgia Standardized Test Practice Workbook Copyright © McDougal Littell Inc. All rights reserved.

LESSON

12.4

GA QCC: 1, 3, 30, 33, 37

Standardized Test Practice

For use with pages 743­749

GHSGT: 2, 4, 9, 20, 26, 35

TEST TAKING STRATEGY

If you find yourself spending too much time on one test question and getting frustrated, move on to the next question. You can revisit a difficult problem later with a fresh perspective.

6. Multiple Choice

1. Multiple Choice

What is the volume of a prism with a rectangular base, with sides of 5 feet and 6 feet, and a height of 4 feet? 60 ft

3

Find the volume of the

oblique prism.

A B C D E

156 cm3 144 cm3 8 cm 180 cm3 62.4 cm3 124.8 cm3

5 cm 6 cm 10 cm

A C E

B D

240 ft

3

120 ft3 480 ft

3

180 ft3

2. Multiple Choice

Find the value of x if the right prism has a volume of 24 m3. 1m 3m 5m

2m

7. Multiple Choice

6m

A C E

B D

2m 4m

x

Find the value of x if the volume of the prism is 105 cm3. 2 cm 3 cm 4 cm 5 cm 6 cm

7 cm 10 cm 8 cm

A B C D E

Chapter 12

3. Multiple Choice

Find the volume of the right cylinder. Round the answer to the nearest hundredth. 4.2 ft 324.59 ft3 216.97 ft3 1996.22 ft3 681.64 ft3 2726.55 ft3

x

A B C D E

8. Multiple Choice

12.3 ft

Find the value of x, if the volume of the cylinder is 301.6 in.3. 1.5 in. 3 in. 4.5 in. 5 in. 6 in.

8 in. 4 in.

A B C D E

x

4. Multiple Choice

Find the volume of a prism that has a height of 10.5 m and has a right triangle for a base. The legs of the triangle are 5 m and 7 m. Round answer to nearest hundredth. 183.75 m3 367.5 m3 180.04 m3

B D

9. Multi-Step Problem

A C E

225.80 m3 316.14 m3

You have two containers. One is a cylinder with a height of 15 inches and a diameter of 10 inches. The other side is a cube with sides of 12 inches.

a. Sketch the containers. b. Find the volume of the cylinder.

5. Multiple Choice

A cylinder has a radius of 24.6 in. and a volume of 29,468 in.3. Find its height. 14.5 in. 16 in.

B E

c. Find the volume of the cube. d. How many gallons of water are needed to

A D

15.5 in. 16.5 in.

C

15 in.

fill the cylinder? (Hint: 1 gallon of water is 0.1337 ft3.)

Geometry

Georgia Standardized Test Practice Workbook

Copyright © McDougal Littell Inc. All rights reserved.

81

LESSON

12.5

GA QCC: 1, 3, 30, 33, 37

Standardized Test Practice

For use with pages 752­758

GHSGT: 4, 9, 20, 26, 35

TEST TAKING STRATEGY

The mathematical portion of the SAT is based on material taught in your high school mathematics courses. One of the best ways to prepare for the SAT is to keep up with your regular studies and do your homework.

4. Multiple Choice

1. Multiple Choice

Find the area of the base of the pyramid. The base is a regular hexagon. Round to the nearest tenth. 187.1 in.2 432.0 in.2 374.1 in. 498.8

2

Find the value of x if the volume is 113.1 m3. Round to the nearest tenth. 1.7 m 3.0 m 3.1 m 1.8 m 2.4 m

x

12 cm

A B C D E

A

18 in.

B C D

15 in.

249.4 in.2 in.2

12 in.

E

2. Multiple Choice

Chapter 12

Find the volume of the cone. Round to the nearest tenth. 1470.3 in.3 545.3 in. 490.1 in.

3

Quantitative Comparison In Exercises 5 and 6, use the diagram of the solids to choose the statement below that is true about the given values.

A B C

A B C D E

The value in column A is greater. The value in column B is greater. The two values are equal. The relationship cannot be determined from the given information. Column A

7 in.

1960.4 in.3

3

13 in. 12 in.

D

5881.1 in.3

Column B

15 in.

3. Multiple Choice A B C D E

Find the volume of the pyramid. Round to the nearest tenth. 33.3 cm3 141.4 cm3 100 cm3 47.1 cm3 37.5 cm3

5 cm 8 cm 5 cm 9 cm 12 in.

10 in.

5. 6.

Area of base Volume

Area of base Volume

82

Geometry

Georgia Standardized Test Practice Workbook

Copyright © McDougal Littell Inc. All rights reserved.

LESSON

12.6

GA QCC: 3, 30, 33, 37

Standardized Test Practice

For use with pages 759­765

GHSGT: 9, 20, 26, 35

TEST TAKING STRATEGY

Staying physically relaxed during the SAT is very important. If you find yourself tensing up, put your pencil down and take a couple of deep breaths. This will help you stay calm.

6. Multiple Choice A B C D E

1. Multiple Choice A C E

If a plane contains the center of a sphere, then the intersection is called a hemisphere. semi-circle. half-circle.

B D

Find the surface area of the hemisphere. Round to the nearest tenth. 706.9 cm2 1413.7 cm2 2120.6 cm2 3534.3 cm2 7775.5 cm2

15 cm

diameter. great circle.

2. Multiple Choice A B C D E

Find the surface area of the sphere. Round to the nearest tenth. 175.9 in.2 615.6 in.2 307.8 in.2 461.8 in.2 1436.8 in.2

7 in.

Quantitative Comparison In Exercises 7 and 8, use the diagrams to choose the statement that is true about the given values.

Chapter 12

A B C

The value in column A is greater. The value in column B is greater. The two values are equal. The relationship cannot be determined from the given information. Column A Column B

6 cm

3. Multiple Choice A B C D E

Find the volume of the sphere. Round to the nearest tenth. 44,602.2 m3 1520.5 m3 1393.8 m3 5575.3 m3 1858.4 m3

7.

22 m

D

5 cm

Surface Area Volume

Surface Area Volume

4. Multiple Choice A C E

What is the radius of a sphere with surface area of 1963.5 cm2? 11 cm 11.5 cm 13 cm

B D

8.

12.5 cm 12 cm

5. Multiple Choice

Find the circumference of the great circle if the volume of the sphere is 179.6 m3. Round to the nearest tenth.

A C E

22 m 11 m 26.6 m

B D

23.8 m 11.9 m

Geometry

Georgia Standardized Test Practice Workbook

Copyright © McDougal Littell Inc. All rights reserved.

83

LESSON

12.7

GA QCC: 3, 30, 33

Standardized Test Practice

For use with pages 766­772

GHSGT: 20, 26, 35

TEST TAKING STRATEGY

When checking your work, try to use a method other than the one you originally used to get your answer. If you use the same method, you may make the same mistake twice.

6. Multiple Choice

In Exercises 1­3, use the similar figures below.

3 4.5 4 2 3 6

Which solids below are III.

10 3

similar? I.

5 2 2 3 3

9 2

II.

Figure A

4 3

8

Figure B 1. Multiple Choice

Find the scale factor for

B E

solid A to solid B.

A

1:2 2:3

1:3 2:5

C

1:4

A C

Chapter 12

D

I and II II and III none of these

B D

I and III I, II, and III

2. Multiple Choice A D

Find the ratio of the surface areas for A to B. 4:9 1:4

B E

E

1:9 1:16

C

4:25

7. Multi-Step Problem

Use the similar solids

shown below.

9.9 in. 13.2 in.

3. Multiple Choice A D

Find the ratio of the volumes for A to B. 1:27 8:125

B E

1:8 1:64

C

8:27

A

15 in.

B

4. Multiple Choice

Two prisms are similar with a scale factor of 1:4. Find the volume of the first given that the volume of the second is 2400 ft3. 600 ft 300

3

a. What is the scale factor of prism A to

prism B?

b. What is the height of prism B? c. What is the volume of prism B if the

A C E

B D

37.5 ft 75 ft3

3

150 ft3 ft3

volume of prism A is 367.5 in.3?

d. What is the surface area of a third prism

5. Multiple Choice

Two pyramids are similar with a ratio of surface areas of 25:64. Find the volume of the second pyramid given that the first has a volume of 250 m3. 61.0 m3 1024 m3 4194 m3

Geometry

Georgia Standardized Test Practice Workbook

that is similar to A and B, and has a volume of 45.94 in.3?

A C E

84

B D

640 m3 97.7 m3

Copyright © McDougal Littell Inc. All rights reserved.

Georgia End-of-Course Practice Test

For use after Chapters 1­12

1. Multiple Choice A D

Find the length of AC if AB is 8, BC is 13, and B is between A and C. 5 18

B E

6. Multiple Choice A C E

What is the value of x?

4x 6x 3 6

5 4 8

B D

4.5 1

8 21

C

13

2. Multiple Choice A C E

Find the measure of

1.

7. Multiple Choice

5x

2

48 52 42

B D

50 32

1 100 48

XY is the perpendicular bisector of AB. Find AO and AY. AO AY AO AY AO AY AO AY AO 12, 4 8, 4 16, 4 8, 19 16, AY

A

3 x 2

A B C D E

3. Multiple Choice

Which property of equality matches the conditional statement "If WX XY and XY YZ, then WX YZ?" Addition property Symmetric property Reflexive property Substitution property Transitive property

Y

2y 11

O

3y

7

A B C D E

X

4

1 x 2

B

12

19

8. Multiple Choice 4. Multiple Choice

Find the values of x and y

t

2(2y 1) (3x 4)

bisectors of

A

In the diagram, the angle ABC meet at point D. Find DG.

A E D F 80 cm

when a b.

A B C D E

10 cm 15 cm 20 cm 30 cm 35 cm C

x y x y x y x x 2.

27.3, 22 30, 22 27.3, 43.5 30, y 30, y

a

B C

b

86

D E

G B 50 cm

43.5 21 Find the measures of

50

9. Quantitative Comparison A

Choose the statement below that is true. The value in column A is greater. The value in column B is greater. The two values are equal. The relationship cannot be determined from the given information.

5(y 2)

5. Multiple Choice

1

and

A B C D E

B C D

m 1 m 2 m 1 m 2 m 1 m 1 m 1

80 , 130 50 , 100

1

2

65 , m 2 65 , m 2 50 , m 2

115 100 115

Column A Column B y x

35

2(x

10) 110

55

Copyright © McDougal Littell Inc. All rights reserved.

Geometry

Georgia Standardized Test Practice Workbook

85

Georgia End-of-Course Practice Test

For use after Chapters 1­12

10. Multiple Choice

Name the type of transformation and the coordinates corresponding to point A . rotation about 0, 1 ; 1, 5 rotation about 1, 1 ; 3, 5 reflection in line y 1; 1, 5 reflection in line y 2; 2, 5 translation in line y 1; 2, 5

C A B

y

14. Multiple Choice A

Solve

B E

6 x 5 x

C

3 1

.

A B C D E

5 6

7 5.3

8 3

A

1

B

D

C

1 x

15. Multiple Choice

In the diagram,

D

AB BD

AC . EC

Find the length of AE.

A C E

8 1 5 3 1 13 3

B D

4 12

4

B

6

E

C

8

A

11. Multiple Choice

Given points A 1, 2 and B 5, 6 , find point C on the x-axis so that AC BC is a minimum.

5 2,

16. Multiple Choice

A D

0

B E

2, 0 0, 2

C

3, 0

ABCD ~ EFGH. The perimeter of ABCD is 16. What is the length of BC?

B C E

5 8

0, 3

A D

F

7 12

12. Multiple Choice

The coordinates of ABC are A 3, 2 , B 1, 6 , and C 2, 3 . The component form of HJ is 2, 6 . What are the coordinates of A B C after the translation using HJ ?

\ \

H

G

A D

3.5 4

B E

2.5 5

C

6

A B C D E

A 5,

4 , B 1,

12 , C 4, 9 4, 3 9 12 , C 2,

9

17. Multiple Choice

Find the length of x in the

A 5, 4 , B 1, 0 , C 0, A 5, 8 , B 1, A 5, A 6, 12 , B 4 , B 1, 0 , C 0,

diagram.

A B

6.9 m 8.4 m 5.25 m 6.25 m 10.5 m

10 m 14 m

36 , C

4, 18

C D E

x

6m

13. Multiple Choice

Translation 1 maps A to A . Translation 2 maps A to . What translation maps A to A ? 2, y 1, y 4 4 12 8 8 6 2

Translation 1: x, y x Translation 2: x, y x

A B C D E

86

18. Multiple Choice A C E

Find the value of x. Round to the nearest tenth if necessary. 7.2 7.5

10

x, y x x, y x x, y x x, y x x, y x

Geometry

1, y 3, y 2, y 1, y 3, y

B

5.6 4.8

8

13.3 D

x

6

Georgia Standardized Test Practice Workbook

Copyright © McDougal Littell Inc. All rights reserved.

Georgia End-of-Course Practice Test

For use after Chapters 1­12

19. Multiple Choice

Find the value of y. Round to the nearest tenth if necessary. 5.7 11.5

B

25. Multiple Choice A

16

Find the value of x.

(7x 15)

25 10 45

B D

20 15

y

A C E

8.0 13.9

8

C E

12.6 D

(3x

15)

26. Multiple Choice 20. Multiple Choice A C E

Find m 1.

Find the value of x that makes the triangle obtuse. 27.8 8 13 8 7

B D

A C

90 75 15

B D

45 60

120 30 1

7 15 7 14

17

x

32

E

21. Multiple Choice

The side of an equilateral triangle is 11 cm. Find the length of an altitude of the triangle.

11 2 11 2

27. Multiple Choice A B C D

Find the values of x and y. Round to the nearest tenth. x x x x x 10, y 12, y 19.4, y 10, y 12, y 7.7 7.7 7.1 7.1 7.1

5 6 3

y

A D

B

8.3

11 2

C

7.8

x

2

E

3

12

22. Multiple Choice A B C D E

Find the area of the triangle. Round to the nearest tenth. 77.6 cm2 47.3 cm2

11 cm 38

E

28. Multi-Step Problem

is h,

The center of a circle 2 and its radius is 4.

94.6 cm2 155.1 cm2 82.5 cm2

a. If another point on the circle is 3, 2 ,

what is the value of h? b. What is the equation of the circle in standard form? c. Graph the equation.

29. Multiple Choice

23. Multiple Choice

Find m A. Round to the

A B

nearest tenth.

A C E

28.1 48.6 41.4

B D

61.9 59.2

25.5 22.5

What is the sum of the measures of the interior angles of a convex 17-gon? 2340 2880

B E

A D

2520 3060

C

2700

24. Multiple Choice If LK is tangent to find JL.

A C E

C

J,

30. Multiple Choice A

Find the area of the regular pentagon. Round to the nearest tenth. 48.8 61.9 60.0

B D

7 9 11

B D

8 10

54.6 78.5

5

J

9

C E

K

L

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Geometry

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87

Georgia End-of-Course Practice Test

For use after Chapters 1­12

31. Multiple Choice

A regular octagon has an area of 81 ft2. Find the scale factor of this octagon to a similar octagon with an area of 625 ft2. 3:5 8:625

B E

36. Multiple Choice

Find the volume of the sphere in Exercise 35. Round to the nearest tenth. 301.6 in.3 603.2 in.3 3619.1 in.3

B D

A C E

7238.2 in.3 1809.6 in.3

A D

9:25 64:390,625

C

27:125

32. Multiple Choice A B C D E

Find the area of Round to the nearest tenth. 89.8 cm2 44.9 cm 80.1

2

C.

8.1 cm 65

Quantitative Comparison In Exercises 37­39, use the diagrams below to choose the statement that is true about the given value.

A B C D

The value in column A is greater. The value in column B is greater. The two values are equal. The relationship cannot be determined from the given information. Column A

6m 8m

cm2

2

C

134.7 cm2 160.2 cm

33. Multiple Choice A C E

Find the diameter of B, if the area of the shaded region is 32.07 in.2. 3.5 in. 14 in. 24.5 in.

B D

Column B

15 m

7 in. 49 in.

75

11 m

34. Multiple Choice

Find the probability that a point chosen at random in the circle lands in the shaded region. Round to the nearest tenth. All shaded regions have a central angle equal to 15 . 25% 33.3% 50%

B D

37. 38. 39.

Lateral area Surface area Volume

Lateral area Surface area Volume

A C E

30% 42%

35. Multiple Choice A B C D E

Find the surface area of the sphere. Round to the nearest tenth. 301.6 in.2 7238.2 in.2 603.2 in.2 1809.6 in.2 3619.1 in.2

12 in.

88

Geometry

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ANSWERS

Chapter 1

Section 1.1

1. C 2. B 3. C 4. D 5. B 6. C 7. a. row 5: 1, 4, 6, 4, 1; row 6: 1, 5, 10, 10, 5, 1 b. The first and last number in each row is 1. Every other number in each row is formed by adding the two numbers immediately above the number. c. Each row has one more entry than the previous row.

Answers

Section 1.7

1. C 8. D 2. B 9. C 3. D 10. A b. 180 in. 4. C 5. E 6. E 7. C

11. a. 2000 in.2

c. 2279 in.2; 192 in.; about 14.0%

Chapter 2

Section 2.1

1. C 2. B 3. A 4. D 5. E 6. B 7. a. If there are three noncollinear points, then there is exactly one plane containing those points. b. If there is exactly one plane containing three points, then they are noncollinear points. c. If there are not three noncollinear points, then there is not exactly one plane containing them. d. If there is not exactly one plane containing three points, then the three points are not noncollinear. e. yes

Section 1.2

1. D 8. B 9. a.

B A D A E C B F D H C G

2. E

3. B

4. E b.

5. E

6. B

7. B

c.

B F A E D H C G

d. rectangular prism

Section 2.2

1. E 2. B 3. D 4. A 5. D 6. B 7. D

Section 2.3

1. C 2. A 3. E 4. C 5. D 6. C 7. a. If you get caught exceeding the speed

Section 1.3

1. E 8. A 2. B 9. C 3. D 10. D 4. B 5. A 6. C 7. C 11. A 12. A 13. D

Section 1.4

1. C 8. C 2. A 3. D 4. C 5. B 6. B 7. A

limit, then you will get a speeding ticket. b. If you get a speeding ticket, then you will pay higher insurance rates. c. If you do not get a speeding ticket, then you do not get caught exceeding the speed limit; ~q ~p d. If you get caught exceeding the speed limit, then you will pay higher insurance rates; statement p must be true for q and r to be true.

Section 2.4

Section 1.5

1. C 8. E 2. B 9. C 3. D 10. B 4. A 5. B 6. B 7. C

1. E

2. B

3. C

4. B

5. A

6. D

7. a. Angle addition postulate c. Substitution property e. Substitution property

b. given

d. given f. Distributive property

Section 1.6

1. D 8. C 2. D 9. C 3. D 10. C 4. C 5. C 6. B 7. B

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Geometry

Georgia Standardized Test Practice Workbook

A1

Answers continued

Answers

g. Given that m ABE m EBC and m EBD m DBC, it can be shown that m ABE 2 m EBD using the angle addition postulate, substitution property, and distribution property of equality. b. Statements 1. a n 2. 3 4 Reasons 1. Proven in part (a). 2. Alt. int.

Section 2.5

1. E 8. B 2. D 3. C 4. B 5. E 6. C 7. B

Theorem 3. 4 is a right angle. 3. Transitive Prop. of 4. b n 4. Def. of perp. lines

Section 3.6

1. B 8. B 2. D 9. B 3. C 4. C 5. E 6. A 7. A

Section 2.6

1. D 8. B 2. E 9. C 3. D 10. A 4. C 5. A 6. B 7. D

Section 3.7

1. B 8. a. 2. E

y

3. C

4. A

5. A b. y c. y d. y

6. C

1 3x 1 3

7. E

Chapter 3

Section 3.1

1. E 8. A 2. E 3. B 4. D 5. C 6. C 7. E

1 1

B(5, 2) A(2, 1)

x

3x 3x

1 3

7 17

e. m

c. AB, EF, BC, FG

Section 3.2

1. B 8. A 2. D 3. C

9. a. EH, FG, BC

b. DC, AB, AE, DH d. all of parts (a) and (c)

Chapter 4

Section 4.1

1. E 8. E 2. C 9. B 3. D 4. C 5. D 6. D 7. B

4. E

5. C

6. C

7. B

Section 4.2

1. C 8. B 3. B 4. B 5. C 6. C 7. A 2. D 3. B 4. A 5. D 6. E 7. A

Section 3.3

1. E 8. C 2. C

Section 4.3

1. E 8. B 3. E 4. B 5. D 6. A 2. C 9. D 3. A 10. C 4. A 5. C 6. E 7. A 11. D Reasons

Section 3.4

1. B 2. D

12. Sample answers: a. Statements 1. AB 2. AD 3.

Section 3.5

1. C 2. A 3. E 4. A 5. E 6. D 7. Sample answers: a. Statements 1. a b, m n, 2. 3. 4. 5. Reasons 1. Given 2. Def. of perp. lines 3. Corresp. Post. 4. Transitive Prop.

AF, BD AD ADB

FD

1. Given 2. Reflexive Prop.

ADF

m 1 is a right angle. 3 1 3 is a right angle. a n

a

of Congruence 3. SSS Congruence Postulate

of

5. Def. of perp. lines

A2

Geometry

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Answers continued

14. a. Statements b. Statements 1. Reasons Reasons 1. Given 2. Reflexive

Answers

DAB FE FE BC BC FE AC

DAF

1. Corresp. parts of 2.

2. BC 3. AF

AB 4. AF

5. AF 6. AE 7.

AE; AC AC AC

3. 4. 5. 6.

ACD

AED

7.

triangles are . Given Segment Add. Postulate Substitution property of equality Substitution property of equality Transitive property of equality SAS Congruence Postulate

1 2 2. AG

1.

3, 4 AG

3.

AGC

Property of Congruence AGE 3. AAS Congruence Theorem

Reasons

b. Statements 1.

1. Given 2 4 2. BGC FGE 2. Vert. Angles Thm. 3. GC GE 3. Corresp. parts of triangles are . 4. BEG FEG 4. ASA Congruence Postulate c. Statements 1. GD 2. Reasons 1. Reflexive Prop.

c. Statements 1. CD 2.

Reasons 1. Corresp. parts of

ED FED

GD

BCD

triangles are . 2. SSS Congruence Postulate

of Congruence AGC AGE, GC GE m AGE m CGD m EGD m EGD CGD EDG

5. Substitution 2. Corresp. parts

Section 4.4

1. C 2. D 3. B 4. D 5. A 6. D 7. C 8. Sample answers: a. Statements 1. AB CD, Reasons 1. Given

3. m AGC 4. m AGC

CB DE, AB CD 2. ABC BCD, BCD CDE 3. ABC CDE

4. 5.

2. Alt. int. Angles

BAC ABC

DCE CDE

Theorem 3. Transitive prop. of equality 4. Corresp. 5. ASA Congruence Postulate

Reasons 1. Corresp. parts of

180 , m AGE 180 5. m AGC 180 6. EGD

7.

triangles are . 3. Def. of congruence 4. Def. of linear pair

CDG

prop. of equality supp. to same are . 7. SAS Congruence Postulate

6. 2

Section 4.6

1. B 8. D 2. D 9. A 3. E 4. B 5. A 6. D 7. C

b. Statements 1. AC 2. AC

CE

CE 3. C is midpoint of AE.

Section 4.5

1. D 8. C 2. C 9. A 3. C 10. E

triangles are . 2. Def. of 3. Def. of midpoint

Section 4.7

1. D 8. C 2. B 3. C 4. D 5. B 6. E 7. A

Chapter 5

Section 5.1

4. C 11. E 5. D 6. A 7. B 1. E 2. C 3. B 4. A 5. A 6. A 12. B 13. C

Geometry

Georgia Standardized Test Practice Workbook

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A3

Answers continued

Answers Section 6.2 Section 5.2

1. B b. 2. B

y

1. C 3. B 4. A 5. C

5

2. E

3. B

4. B

5. D

6. E

7. A

6. E

8. C

7. a. circumcenter c. 4, 2 d. about 2.5 miles

Section 6.3

1. E 2. D 3. C 4. C

1 3,

5. C

3 2,

6. B

1 1 x

Section 5.3

1. B 8. B 2. D 9. D 3. E 4. A 5. B 6. C 7. A

so BD The slope of AD and CB is so AD CB. b. AD CB 10, so AD CB; CA BD 13, so CA BD 4 7 c. equation for CD: y 5x 5; 2x 14; equation for AB: y lines intersect at E AE EB 5 2

11 2,

7. a. The slope of BD and AC is

AC;

3 ; CE

ED

3;

Section 5.4

1. A 8. C 2. D 3. E 4. C 5. B 6. C 7. B

Section 6.4

1. B 8. D 2. B 9. A 3. D 10. C 4. E 5. E 6. A 7. C

Section 5.5

1. C 8. A 2. A 3. D 4. D 5. B 6. E 7. A

Section 6.5

1. B 8. A 2. C 3. C 4. D 5. D 6. A 7. B

Section 5.6

1. E 6. a. 2. C 3. D

B

4. B

5. A

Section 6.6

1. A 7. a.

3 2

2. D b. 1

3. C

4. C

5. D

6. B

A

C B

b.

A

C

D

c. 125

d. BC

e. m BCD

m A

m B

EF because opposite sides of rectangle are congruent. m DGF m EFG 90 by def. of a rectangle. m EFC m EFG 180 and m DGA m DGF 180 because linear angles are supplementary. m DGA 90 180 and m EFC 90 180 by Substitution Prop. of Equality. m DGA m EFC 90 by Subtraction Prop. of Equality. m A m B m C 60 because regular triangles have 3 congruent angles. ADG CEF by AAS.

c. DG

Chapter 6

Section 6.1

1. A 8. B 2. C 3. D 4. D 5. E 6. C 7. D

Section 6.7

1. D 2. B 3. A b. 92 4. C 5. E 6. D 7. A 8. a. 20

ft2

in.2

c. 11.25

ft2

A4

Geometry

Georgia Standardized Test Practice Workbook

Copyright © McDougal Littell Inc. All rights reserved.

Answers continued

Section 7.6 Answers

Cumulative Review

Chapters 1­6

1. B 2. C 3. C 4. D 5. A 6. B 7. A 8. C 9. a. If you stay up late, then you are tired. b. If you are tired, then you are cranky. c. ~q ~p; if you are not tired, then you did not stay up late. d. If you stay up late, then you are cranky. 10. C 11. E 12. D 13. B 14. C 15. A 16. B 17. D 18. C 19. A 20. D 21. B 22. B 23. E 24. D 25. E 26. C 27. C 28. D 29. A 30. D 31. B 32. B 33. B

1. C

2. B

3. E

4. E

5. B

6. A

7. Sample answers: a. b.

c.

d.

Chapter 7

Section 7.1

1. D 2. C 3. B 4. D 5. B 6. A

Chapter 8

Section 8.1

1. B 3. E 4. C 5. B 6. E 7. A 8. C 2. C 9. A 3. B 4. D 5. E 6. E 7. C

Section 7.2

1. D 2. B 8. a. A 1,

B 5,

y 1 1

4, 6 , C 3, 1

C

x

b. A B

Section 8.2

1. D 8. A 2. C 9. B 3. C 10. C 4. D 5. E 6. D 7. C

Section 8.3

A

1. C

B

2. B

3. D

4. E

5. D

6. A

7. C

8. C d. A

c. A

B

B

1, 4 , 5, 6 , C

y

3, 1

B

B

3, 4 , 1, 6 , C

y

Section 8.4

1, 1

1. C

2. B

5 13

3. D

4. A

5. E

6. a. 6.4

b. 3.75 c. d. 20.3 e. Sample answer: Show that the ratio of all sides 0.625.

A

A

1 1 x 1

Section 8.5

1. A

x

C

C

1

2. C

3. D

4. E

5. B

6. C

Section 8.6

e. 1, 0 1. D 8. A 3. D 4. E 5. C 6. A 7. A 2. C 2. E 3. B 4. A 5. C 6. B 7. A

Section 7.3

1. B

Section 8.7

1. A 2. E 3. C 4. B 5. D

Section 7.4

1. C 2. D 3. B 4. E 5. D 6. B

Section 7.5

1. C 2. A 3. A 4. B 5. D

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A5

Answers continued

Answers Section 9.5

6. a.

y

1. A

B

2. C 9. B

3. B

4. E

5. D

6. B

7. C

A

8. B

Section 9.6

C

1 1 x

1. D 8. A

2. C 9. B

3. C

4. B

5. E

6. A

7. B

Section 9.7

b.

y

B' A'

A 2, 10 , B 6, 12 , C 6, 6

c. 6

1. D 8. E

2. A

3. C

4. E

5. B

6. A

7. B

9. a. about 680 mi h; 48.6 NE from horizontal b. about 361 mi h; 33.8 NW from horizontal c. 735 mi h; 43.9 NE from horizontal

C'

x

d. 297 mi h; 42.2 NW from horizontal

d.

y

A

B''

A''

B C

C''

1 5 2, 2 , 3 2, 3 , 3 3 2, 2

Chapter 10

Section 10.1

1. B 2. D 3. B 4. E 5. D 6. A 7. E 8. a. 2, 3 , 3 b. 5, 0 , 3 c. 2, 0 , 5, 3

d. two external tangents; y

x

x

10,

y

x

1

e.

2

f. 4

Section 10.2

1. C 2. B 9. A 3. D 10. C 4. D 5. B 6. C 7. E 8. C 3. E 4. A 5. B 6. C 7. C

Chapter 9

Section 9.1

1. C d. 2. D 8. a. 9.8 ft b. 17.8 ft c. 12.3 ft

Section 10.3

1. D 8. E 2. B 9. C 3. C 10. B 4. A 5. C 6. D 7. B

HTG ~

AHG ~

ATH

Section 10.4

1. B 2. C 9. A 3. E 10. B 4. A 5. D 6. C 7. B

Section 9.2

1. D 8. A 2. D 3. B 4. C 5. D 6. D 7. A

8. D

Section 10.5 Section 9.3

1. C 8. A 2. E 9. B 3. B 4. A 5. C 6. A 7. D 1. A 8. B 2. B 9. A 3. E 4. D 5. D 6. A 7. C

Section 10.6 Section 9.4

1. D 8. A 9. a. 5 d. 5 units

A6

1. E 3. A 4. E 5. C 6. C 7. B 8. D

2. C

3. D

4. C

5. D

6. B

7. A

2. C

2 units

e.

b.

5 2 units 2

c.

5 units 2

5 3 units f. 32.2 square units 2

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Georgia Standardized Test Practice Workbook

Answers continued

Chapter 12

9. a. c.

Answers

1

b. x

y

1

y 2 9 d. Sample answers: 1, 5 ; 0, 0 ; 5, 0

2

2

Section 12.1

1. E 8. A 2. C 3. C 4. B 5. B 6. C 7. E

1 2 x

Section 12.2

1. D 8. A 2. B 9. A 3. B 4. A 5. C 6. D 7. E

Section 10.7

1. B 8. a.

2 2 x

Section 12.3

3. C

A(4, 6)

2. E

y

4. E

5. A

6. E

7. D

1. C 8. a.

2. B

3. E

10.33

4. D

5. A

6. E

2

7. E

b. 92.97 in. d. 1:4

6

c. 108.57 in.2

B ( 2,

4) C (10,

4)

b. A: x

4 2 10 4

2 2

2

y y y 4

2

6 4

2

2

100 36 36

Section 12.4

1. C 8. E 9. a.

5 12 15

B: x C: x c. 4,

2. B

3. D 4. A 5. B

6. E

7. B

Chapter 11

Section 11.1

1. B 8. E 2. A 9. B 3. C 10. B 4. D 5. D 6. C 7. B b. 1178.1 in.3 4. A 5. C 6. C 7. B

12 12

c. 1728.0 in.3

Section 11.2

1. E 8. B 2. B 3. B

d. about 5.1 gallons

Section 12.5

1. C 2. D 3. A 4. B 5. A 6. A

Section 11.3

1. B 2. D 3. C 4. B 5. D c. 4:5 6. A 7. E 8. a. 1200 ft2 e. $1440 b. 1500 ft2 d. 240 ft

Section 12.6

1. D 2. B 3. D 4. B 5. A 6. C 7. B 8. A Section 12.7 1. D 2. A 3. C 4. B 5. C

3

Section 11.4

1. B 8. D 2. A 9. A 3. D 4. C 5. A 6. E 7. D

6. A

7. a.

1:4 3

b. 20 in.

c. 871.1 in.

d. 101.8 3. B 4. B 5. E 6. C 7. D

in.2

Section 11.5

1. E 8. B 2. D 9. B

Section 11.6

1. D 2. D 3. A 4. B 5. E 6. C 7. A

Georgia End-of-Course Practice Test 1. E 2. D 3. E 4. B 5. C 6. A 7. E 8. D 9. A 10. C 11. B 12. D 13. B 14. B 15. E 16. A 17. C 18. D 19. D

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Georgia Standardized Test Practice Workbook

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Answers continued

Answers

20. C 25. D c.

1 1 x y

21. E 26. B b. x

22. A 27. A

23. B

24. B

28. a. 3

3

2

y

2

2

16

29. C 35. D

30. E 36. B

31. B 37. B

32. E 38. A

33. C 39. A

34. C

A8

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