Rotational Symmetry. What is the order of rotational symmetry of a rectangle?

How To Work Out The Order Of Rotational Symmetry Video


A shape has rotational symmetry if you can rotate the shape onto itself more than once in a full 360⁰ turn. The amount of times you can turn the shape onto itself is known as the order of rotational symmetry. If a shape has rotational symmetry order 1, then the shape has no rotational symmetry, as the shape only fits onto itself once in a full 360⁰ turn (that is at the end only). A shape of rotational symmetry of order 2 or more means that you can rotate the shape onto itself 2 or more times in a full 360⁰ turn (so the shape has rotational symmetry).

The easiest way to find the order of rotational symmetry is to trace the shape and turn the tracing paper 360⁰, counting the amount of times the shape on the tracing paper fits onto the original shape. Make sure that you only turn the tracing paper around once, so it’s a good idea to trace your shape so that the tracing paper is level with your page.

Example 1

What is the order of rotational symmetry of a rectangle?

A rectangle will fit onto itself twice (one at 180⁰ and the other at the end), therefore, a rectangle has order 2 rotational symmetry.

Example 2

What is the order of rotational symmetry of an equilateral triangle?

An equilateral triangle will fit onto itself 3 times in a 360⁰ turn, so the order of rotational symmetry is of order 3.

Example 3

What is the order of rotational symmetry of a scalene triangle?

A scalene triangle will only fit onto itself once in a full turn (only at the end). So the order of rotational symmetry of a scalene triangle is 1, therefore, a scalene triangle does not have rotational symmetry.

Example 4

What is the order of rotational symmetry of a regular pentagon?

The order of rotational symmetry for a regular pentagon is 5, as it will rotate 5 times onto itself in a full turn. Another point to note is that the order of rotational symmetry is equal to the amount of sides if the shape is regular (regular means equal side lengths and angles). So for example, if you had a regular decagon, then the order of rotational symmetry of the regular decagon will be 10.

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Comments 1 comment

anushka 3 years ago

it helped me very much because i didn't understand rotational symmetry.

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