EDEXCEL GCSE FOUNDATION MATHS - What is Rotational Symmetry

Edexcel GCSE Foundation Maths: Rotational Symmetry

What is Rotational Symmetry?

Rotational symmetry is when a shape can be rotated less than 360 degrees and still look exactly the same. The number of times it looks the same in a full rotation is called the order of rotational symmetry.

Think of it like spinning a wheel:

• If the wheel has 4 equal sections, you can rotate it 4 times before it looks exactly the same as it started. This shape has order 4 rotational symmetry.

• If the wheel has 3 equal sections, you can rotate it 3 times before it looks exactly the same as it started. This shape has order 3 rotational symmetry.

How to Identify Rotational Symmetry

1. Trace the shape: Make a tracing of the shape on a piece of paper.
2. Rotate the tracing: Rotate the tracing around its center point.
3. Count the rotations: Count how many times the tracing looks exactly the same as the original shape before completing a full 360-degree rotation. This is the order of rotational symmetry.

Examples

• Square: Has order 4 rotational symmetry (looks the same after rotations of 90°, 180°, and 270°).
• Equilateral Triangle: Has order 3 rotational symmetry (looks the same after rotations of 120° and 240°).
• Rectangle: Has order 2 rotational symmetry (looks the same after a 180° rotation).
• Circle: Has infinite order rotational symmetry (looks the same after any rotation).

Key Points

• Order of Rotational Symmetry: The number of times a shape looks the same during a full rotation.
• Center of Rotation: The point around which the shape is rotated.
• Angle of Rotation: The amount of degrees the shape is rotated.

Practice

Identify the order of rotational symmetry for the following shapes:

1. A regular pentagon
2. A rectangle
3. A semi-circle
4. A star with five points

Challenge:

Can you draw a shape that has order 6 rotational symmetry?