Unit 15 Section 3 : Symmetry
In this section we revise the symmetry of objects and examine the symmetry of regular polygons.
There are two types of symmetry: reflective symmetry and rotational symmetry.
Look for lines of symmetry in the two shapes below:
Here are the shapes with the lines of symmetry drawn on:
The order of rotational symmetry is the number of times an object looks the same as it did originally when it is rotated through 360°. Even if a shape appears to have no rotational symmetry then the order of rotational symmetry will still be 1, because every shape looks the same at the end of a 360° rotation as it did originally.
There is a centre of rotation about which the rotational symmetry occurs. There can only be one centre of rotation in a shape.
The three diagrams below show shapes with different orders of rotational symmetry.
Symmetries in regular polygons
The order of rotational symmetry and the number of lines of symmetry of any regular polygon is equal to the number of sides.
ExercisesWork out the answers to the questions below and fill in the boxes. Click on the button to find out whether you have answered correctly. If you are right then will appear and you should move on to the next question. If appears then your answer is wrong. Click on to clear your original answer and have another go. If you can't work out the right answer then click on to see the answer.
For each of the six diagrams below, draw on all the lines of symmetry and mark the centre of rotation point.
Once you have checked these with the button, fill in the order of rotational symmetry for each one and check that too.
Produced by A.J. Reynolds May 2008