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Symmetry, congruence and quadrilaterals

Chapter 21 and 22 Page 248 to 264

Chapter 21 covers Lines of symmetry Rotational symmetry Planes of symmetry Axes of symmetry Congruent shapes Congruent triangles Chapter 22 covers What is a quadrilateral Special quadrilaterals Interior angles Symmetry of quadrilaterals Perimeter and area of quadrilaterals Area of a triangle

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Lines of symmetry

A line of symmetry is where a line divides the shape into half's and they are a mirror image of each other and if you folded one side over the top of the other along the line of symmetry they would match exactly. What lines of symmetry can you see for the shapes below?

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Rotational symmetry Rotational symmetry is where a shape can turn about a point and fit on itself more than once in 360 degrees. The point which you turn the shape around is called the centre of rotation. Rotational symmetry cannot be one it has to be 2, 3 or more (otherwise the shape is considered to have no rotational symmetry)

The order of rotational symmetry tells you how many times the shape can fit on itself within 360 degrees. This includes fitting back to the starting point. What is the order of rotational symmetry for the shapes below

Exercise 22.1 page 249 questions 1, 2 and 5

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Planes of symmetry

We have looked at 2 dimensional shapes i.e. flat and seen lines of symmetry and rotational symmetry In three dimensional shapes we look at planes of symmetry and axis of symmetry Look at the shapes below and identify the planes of symmetry and axis of symmetry

Exercise 22.2 page 251 questions 1, 2 and 4

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Congruent shapes

Congruence or congruent means in plain English exactly the same. For two shapes to be congruent they have to be the same size and shape. Which shapes are congruent below?

Exercise 22.3 page 252 questions 1 and 3

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Congruent triangles To prove triangles are congruent they are four ways. 1. If all three sides of the triangles are the same then they are congruent (SSS) 2. If two sides of the triangles and the angle between them are the same (SAS) 3. Two angles and a corresponding side (ASA or AAS) 4. Right angled triangles only The hypotenuse and one side are the same (RHS)

Exercise 22.4 page 253 questions 1 and 3

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A quadrilateral is a four sided shape. Special quadrilaterals you need to know are Parallelogram, rhombus, rectangle, square, kite, trapezium and isosceles trapezium

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Quadrilaterals angles and symmetry

The Quadrilateral interior angles always add up to 360 degrees Quadrilaterals also have rotational and lines of symmetry

Find and mark the lines and rotational symmetry of a parallelogram, isosceles trapezium, rectangle, square, rhombus, and kite

Exercise 23.1 page 259 questions 9, 10. 11

Exercise 21.2 page 239 questions 1 a b c and 2

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Perimeter and Area of Quadrilaterals

As you know the perimeter means outside of a shape and all you need to do is to add up the sides of the shape to find the perimeter.

Area of a rectangle square are the length times the breadth of the shape. The area of a parallelogram and rhombus is the base times the perpendicular height.

To find the area of a trapezium you add together the parallel sides divide by two and then multiply by the perpendicular height.

Exercise 23.2 page 262 questions 1, 2 and 4

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symmetry and quadrilaterals

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