Symmetry in Real Life
If an object has symmetry or is symmetrical it has a balanced look. There is line symmetry which is similar to an object being seen in a mirror and rotational or turning symmetry which is about rotating objects around thier centre point.




Buildings are often built to look symmetrical.

Designers love to design items with symmetry.

People are often quite symmetrical.

All of these drawings show line symmetry.

There are two types of symmetry: line symmetry, which involves reflection , and rotational symmetry, which involves rotation .
Line Symmetry
A figure has a line of symmetry if it maps or folds onto itself under reflection in the line. The figure is divided by the line into two parts which are identical.
e.g.
Line m is called the mirror line or axis of symmetry.
Different shapes can have various numbers of axes of symmetry. e.g.
Name of shape

Diagram

Number of axes of symmetry

Square



Rectangle



Equilateral Triangle



Rotational Symmetry
A figure has rotational symmetry if it can be rotated around a point, called the centre of rotation so that if fits exactly onto itself.
All figures have an order of rotational symmetry of at least 1.
The order of rotational symmetry is the number of times the shape fits onto itself during a rotation of 360° (one complete turn).
e.g.
Name of shape

Diagram (the dot is the centre of rotation)

Order of rotational symmetry

Square


4
(90°, 180°, 270° and 360°)

Rectangle



Equilateral triangle



Total Order of Symmetry
The total order of symmetry = number of axes of symmetry + order of rotational symmetry.

The table shows the symmetry properties of some common shapes.
Shape 
Axes of symmetry 
Order of rotational symmetry 
Total order of symmetry 
Scalene triangle

0 
1 
1 
Isosceles triangle

1 
1 
2 
Equilateral triangle

3 
3 
6 
Kite

1 
1 
2 
Trapezium

0 
1 
1 
Isosceles trapezium

1 
1 
2 
Parallelogram

0 
2 
2 
Rhombus

2 
2 
4 
Rectangle

2 
2 
4 
Square

4 
4 
8 
Regular pentagon

5 
5 
10 
Regular hexagon

6 
6 
12 
Regular octagon

8 
8 
16 
A figure has point symmetry if it maps onto itself under a rotation of 180° (a half turn). e.g. A parallelogram.
