Understand Rotational Symmetry

In this activity, we will look at rotational symmetry!

 

Rotational symmetry is when a shape looks the same after it has been turned (rotated).

 

Let's use the red equilateral triangle below to demonstrate.

 

 

If we turn it around the point in a clockwise direction for one full 360^o turn it should be the same three times.

See below and watch the X as it turns through 360^o

 

 

 We can see that the triangle is exactly the same three times during a full 360^o turn.

We can say that the equilateral triangle has rotational symmetry of order 3

 

Let's look at another shape.

 

Example

Does the square below have rotational symmetry?

If so, what is the order?

 

 

Answer

Again, we turn it around the centre point 360^o a full turn. (Watch the X.)

 

 

We can see it is exactly the same four times during one full 360^o turn.

We can say that the square has rotational symmetry of order 4.

 

 

If a shape does not have rotational symmetry - it is not the same until it gets back to the top 360^o

This shape does not have rotational symmetry!

 

 

You can see that it wouldn't look the same until it returns to the top again!

 

Let's try some questions on this!