year 8 maths

382 Chapter 6 Angle relationships and properties of geometrical figures 1
6F Line symmetry and rotational symmetry
You see many symmetrical geometrical shapes in nature. The starfish and sunflower are two examples.
Shapes such as these may have two types of symmetry: line and rotational.
Let’s start: Working with symmetry
On a piece of paper draw a square (with side length of about 10 cm ) and a rectangle (with length of about
15 cm and breadth of about 10 cm ), then cut them out.
• How many ways can you fold each shape in half so that the two halves match exactly? The number of
creases formed will be the number of lines of symmetry.
• Now locate the centre of each shape and place a sharp pencil on this point. Rotate the shape 360° .
How many times does the shape make an exact copy of itself in its original position? This number
describes the rotational symmetry.
Key ideas
■ An axis or line of symmetry divides a shape into two equal parts. It acts as
a mirror line, with each half of the shape being a reflection of the other.
This isosceles triangle has one line (axis) of symmetry.
The plural of axis is axes.
A rectangle has two lines (axes) of symmetry.
■ The order of rotational symmetry refers to the number of times a figure
coincides with its original position in turning through one full rotation.
For example, the order of rotational symmetry for an equilateral triangle
is 3, whereas for rectangle it is 2.
■ We say that there is no rotational symmetry if the order of rotational
symmetry is 1 . Right-angle triangles do not have rotational symmetry.
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Cambridge Maths NSW
Stage 4 Year 8 Second edition
ISBN 978-1-108-46627-1 © Palmer et al. 2018
Cambridge University Press
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