Read Microsoft Word  Geometry Honors Final Review with answers 200910.rtf text version
20092010 OCPS End of Course Review for Geometry Honors
You may use a 4function calculator. FCAT Reference Sheets are permissible and recommended. It will be helpful to use your own graph paper to complete some the problems. If you have forgotten a particular skill, the lesson number (for the McDougal Littell Geometry) is provided as a reference for each problem. 1. Write an equation in pointslope form of the line through point J(9, 8) with slope 5. (Section 36)
2. Give the slopeintercept form of the equation of the line that is perpendicular to 7x + 9y = 13 and contains P(10, 3). (Section 37)
3. Complete the proof. Given: Prove:
I
and
(Through out Sections 42 to 44)
K
J
H
L
4. Where can the perpendicular bisectors of the sides of a right triangle intersect?
(Section 52)
5. Three security cameras were mounted at the corners of a triangular parking lot. Camera 1 was 138 ft from camera 2, which was 155 ft from Camera 3. Cameras 1 and 3 were 118 ft apart. Which camera had to cover the greatest angle? (Section 55)
6. Could the lengths given for each of the following be the lengths of the sides of a triangle? Explain your reasoning 7, 25, 10 ; 10, 15, 22 ; 20, 5, 10 ; 15, 9 , 24 (Section 55)
7. Given the coordinates of a triangle are : A (4, 1) ; B ( 3, 5) ; C (1 , 1), graph the triangle: a.) reflect the triangle over the xaxis b.) reflect the original triangle over the yaxis.
(Section 72)
8. Based on the pattern, what is the next figure in the sequence?
(Section 11)
OCPS End of Course Review for Geometry Honors 20092010
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9. Find the distance between points P(2, 1) and Q(4, 2) to the nearest tenth. 10. Name the intersection of plane MOL and plane NOL. 11. Identify the hypothesis and conclusion of this conditional statement: If tomorrow is Monday, then yesterday was Saturday.
(Section 13) (Section 12) (Section 21)
12. Use the Law of Detachment and the Law of Syllogism to draw a conclusion from the three given statements. If a truck weighs more than 2,000 pounds, then it weighs more than Juan's car. If something weighs more than Juan's car, then it is too heavy for the bridge. The truck weighs 2,150 pounds. (Section 23) 13. Name the Property of Equality that justifies the statement: If l = m, then . (need to study all properties) (Section 24)
14.
and
are complementary angles. m
=
, and m
=
. Find the measure of each angle. (Section 16)
15. Line r is parallel to line t. Find m 5. The diagram is not to scale.
r 7 1 t 139° 3 4 2 5
(Section 33)
6
16. Find the values of x, y, and z. The diagram is not to scale.
44° 11° 62° x° z° y°
(Section 41)
17. How many sides does a regular polygon have if each exterior angle measures 45?
(Section 111)
OCPS End of Course Review for Geometry Honors 20092010
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18. Find the missing angle measures. The diagram is not to scale.
111° 110° x° y° 76°
(Section 111)
19. Given
and
, find the length of QS and TV.
(Section 42)
20. What other information do you need in order to prove the triangles congruent using the following Congruence Postulates: a) SAS b) SSS c) ASA d) AAS ? (Sections 43 & 44)
A
B
C
D
21. Find the values of x and y.
A
(Section 41)
y°


x° B
( (
70° D C Drawing not to scale
OCPS End of Course Review for Geometry Honors 20092010
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22. What additional information will allow you to prove ABC DEC congruent by the HL Theorem? (Section 46)
A

B
C
D

E
23. For the parallelogram, if
3 4
and
find
The diagram is not to scale. (Section 62)
2
1
24. In the rhombus, m 1 18 x, m 2 2 x y , m 3 45 z. Find the value of each variable. The diagram is not to scale. (Section 64)

3 2

1

25.
and
R

Find

The diagram is not to scale.
(Section 65)
U

T
26. A map of Europe has a scale of 1 cm to 100 km. If the distance between Paris and Munich is 534 km, how far apart are they on the map, to the nearest tenth of a centimeter? (Section 81)
OCPS End of Course Review for Geometry Honors 20092010


S
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27. Find the geometric mean of the pair of numbers: 72 and 8
(Section 82)
28. Solve for x.
(Section 82)
x
>
x+2 x + 12
>
x+5
29. B is the midpoint of
D is the midpoint of
C
and AE = 25. Find BD. The diagram is not to scale. (Section 54)
B
D
A
E
30.
bisects
Find the value of x. The diagram is not to scale.
E
(Section 51)

)
24° G
D
OCPS End of Course Review for Geometry Honors 20092010
)

6x + 18 F
15x
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31. Write the contrapositive of the conditional statement illustrated by this Venn diagram.
(Section 23)
Cats
Persians
32. Find the value of x. Round your answer to the nearest tenth.
(Section 95)
8
x Not drawn to scale
33. Find the value of x. Round to the nearest tenth.
x 14 Not drawn to scale
(Section 95)
34. An airplane over the Pacific sights an atoll at an angle of depression of 25 . At this time, the horizontal distance from the airplane to the atoll is 4629 meters. What is the height of the plane to the nearest meter? (Section 95)
x
4629 m Not drawn to scale
OCPS End of Course Review for Geometry Honors 20092010
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35.
Find the area. The figure is not drawn to scale.
9 cm 8 cm 15 cm
(Section 17)
9 cm
13 cm
36. Find the area. The figure is not drawn to scale.
(Section 67)
20 in. 12.6 in. 31.5 in.
37. Find the area of the parallelogram. Leave your answer in simplest radical form. (Section 67)
14.5 in.
20 ft 13 ft 12 ft Not drawn to scale
38. A triangle has side lengths of 6 cm, 8 cm, and 9 cm. Classify it as acute, obtuse, or right. (Section 93)
39. Find the area of the regular polygon. Give the answer to the nearest tenth: hexagon with side 6 yd. (Section 112)
OCPS End of Course Review for Geometry Honors 20092010
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40. Find the value of the variable(s). If your answer is not an integer, leave it in simplest radical form. (Section 94)
x 30° 26
y
Not drawn to scale 41. Find the area of an equilateral triangle with side 7. Leave in simplest radical form. (Section 112)
42. Find the area of the figure to the nearest tenth.
(Section 11 5)
135° 5
43. Find the surface area of the cylinder in terms of .
6 in.
(Section 12 2)
18 in.
Not drawn to scale
44. Find the volume of the composite space figure to the nearest whole number.
(Sections 122 to 12 4)
6 mm
11 mm 5 mm Not drawn to scale
OCPS End of Course Review for Geometry Honors 20092010
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45. Find the volume of the sphere shown. Give each answer rounded to the nearest cubic unit.
(Section 12  6)
16 cm
46. Find the value of x. If necessary, round your answer to the nearest tenth. The figure is not drawn to scale. (Section 102)
2x + 63 x2
47. AB = 12, BC = 8, and CD = 5. Find x.
x D C B A
(Section 105)
48. Write the standard equation for the circle.
center (3, 5), r = 2
(Section 106)
49. Given the coordinates of ABC, A( 1, 3) , B (1 , 1) and C (1, 0) , sketch the image of the triangle after the translation: (x , y) ( x 3 , y + 4) (Section 74)
50. A blueprint for a house has a scale of 1 in. : 50 in. A wall in the blueprint is 4 in. What is the length of the actual wall in feet? (Section 82)
OCPS End of Course Review for Geometry Honors 20092010
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Additional Topics to be studied:

all points of concurrency

complementary/ supplementary angles

angle relationships formed by parallel lines and a transversal

properties of parallelograms

proving triangles by SSS, SAS, ASA, and AAS

inverse, converse and contrapositive

special right triangles: 306090 and 4545 90

application of formulas on the reference sheet for area and volume
OCPS End of Course Review for Geometry Honors 20092010
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OCPS Geometry Honors End of Course Review (20092010) Answer Section
1. ANS: y + 8 = 5(x + 9) 2. ANS: y 3. ANS:
9 111 x 7 7
Reason 1.) Given 2.) Vertical Angles Theorem 3.) Angle Side Angle 4.) CPCTC
Statements 1.) H K ; HJ KJ 2.) IJH LJK 3.) IJH LJK 4.) IJ LJ
4. ANS: on the triangle 5. ANS: camera 1 6. ANS: 7, 25 , 10 10, 15 , 22 20, 5 , 10 15, 9, 24 is not a triangle since 7 + 10 < 25 is a triangle is not a triangle since 10 + 5 < 20 is not a triangle since 15 + 9 = 24
7. ANS: a.) A' (4, 1) , B' (3, 5) and C' (1, 1) b.) A' ( 4, 1) , B' ( 3, 5) and C' (1, 1) 8. ANS:
9. ANS: 2.2 10. ANS: OL 11. ANS: Hypothesis: Tomorrow is Monday. Conclusion: Yesterday was Saturday. 12. ANS: The truck is too heavy for the bridge. 13. ANS: Symmetric Property 14. ANS: 15. ANS: 139 16. ANS: 17. ANS: 8 sides 18. ANS: x = 103, y = 70 = 48, = 42
OCPS End of Course Review for Geometry Honors 20092010
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19. ANS: 10 20. ANS: SAS : AC BD SSS :
AB AD
ASA : AC BD and ABC ADC AAS: ABC ADC and BAC DAC 21. ANS: 22. ANS: 23. ANS: 143 24. ANS: x = 5, y = 80, z = 2 or BC EC
25. ANS: 40 26. ANS: 5.3 cm 27. ANS: 24 28. ANS: 2 29. ANS: 12.5 30. ANS: 2 31. ANS: If an animal is not a cat, then it is not a Persian. 32. ANS: 9.5 33. ANS: 15.6 34. ANS: 2159 m 35. ANS: 180.5 cm2 36. ANS: 324.45 in.2 37. ANS: 252 ft2 38. ANS: acute 39. ANS: 93.5 yd
OCPS End of Course Review for Geometry Honors 20092010
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40. ANS: x = 39, y = 41. ANS:
49
4 42. ANS: 29.4 in.2
43. ANS: 288 in. 44. ANS: 438 cm 45. ANS: 2,144 cm (using 3.14 for ) 46. ANS: 9 47. ANS: 27 48. ANS: (x 3) + (y + 5) = 4 49. ANS: A' (4, 1) , B' (2 , 3) and C' (4, 4) 50. ANS: 16.67 feet
OCPS End of Course Review for Geometry Honors 20092010
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