Types of Symmetry
There are two types of symmetry: line symmetry, which involves reflection , and rotational symmetry, which involves rotation.
Type of symmetry

Explanation

Example

Line Symmetry 
A figure has a line of symmetry if it maps or folds onto itself under reflection in the line.

A rectangle has two axis of symmetry. 
Rotational Symmetry 
A figure has rotational symmetry if it maps onto itself as it is rotated about a point at its centre. All figures have an order of rotational symmetry of at least 1. The order of rotational symmetry is the number of times the shape maps onto itself during a rotation of 360°. 
A rectangle has an order of rotational symmetry of 2. 
Total Order of Symmetry 
The total order of symmetry = number of axes of symmetry + order of rotational symmetry. 
A rectangle has total order of symmetry of

The table shows the symmetry properties of some common shapes.
Scalene triangle 

Isosceles triangle 

Equilateral triangle 

Kite 

Trapezium 

Isosceles trapezium 

Parallelogram 

Rhombus 

Rectangle 

Square 

Regular pentagon 

Regular hexagon 

Regular octagon 
A figure has point symmetry if it maps onto itself under a rotation of 180° (a half turn). e.g. A parallelogram.
Click here to test your knowledge of quadrilaterals and triangles.
Tessellations
A tessellation is a pattern where shapes are tiled to fill in all of the available space.
Some examples of tessellations:
Shapes

Tessellation

Shapes

Tessellation


Triangles

Squares and octagons


Quadrilaterals

Combined shapes


Hexagons

Curves (This shape would tessellate!) 