Rotational Symmetry
Rotational symmetry means a shape looks the same after a turn of less than 360° about its centre. The order of rotational symmetry counts how many times it matches in one full turn. For example, a square has order 4.
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What is Rotational Symmetry?
- A shape has rotational symmetry if it looks the same after a turn of less than .
- The shape is rotated about its centre of rotation.
Order and Angle of Rotation
- The order of symmetry is the number of times a shape matches itself in a full turn.
- The angle of rotation = ÷ order (e.g. a rectangle has order 2, so the angle is ).
How to Check for Rotational Symmetry?
- Rotate the shape around its centre and see if it matches its starting position.
- If it matches before , the shape has rotational symmetry.
Practice Questions
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True or False: A rectangle has an angle of rotation of and an order of symmetry of 2.
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A rectangle has a rotational symmetry of , meaning it looks the same after a half turn, and it has an order of symmetry of 2 ( and rotations).
What is the order of symmetry for an equilateral triangle?
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The order of symmetry for an equilateral triangle is 3, as it can be rotated , , and to match its original shape.
If a figure has an angle of rotation of , what is its order of rotational symmetry?
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The order of rotational symmetry is found using , so the figure has an order of rotational symmetry of 3.
A regular octagon has an order of symmetry of 8. What is the angle of rotation?
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The angle of rotation is found using , so the angle of rotation is .
Which of the following shapes has rotational symmetry?
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The circular recycling symbol has rotational symmetry because it looks the same after a certain amount of rotation.
If you rotate a regular pentagon by , will it look the same?
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A regular pentagon has 5 equal sides and angles, giving it rotational symmetry of order 5. Using , it looks the same every turn.
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Students Also Ask
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Rotational symmetry has three key parts. The centre of rotation is the fixed point the shape turns around. The angle of rotation is the smallest turn that makes the shape look the same. The order of rotational symmetry counts how many times it fits onto itself in a full turn.
They are linked by a simple formula using a full turn of 360°. To find the angle of rotation, divide 360° by the order of rotational symmetry. To find the order, divide 360° by the angle of rotation. For example, an order of 3 gives an angle of 120°.
A rectangle has an order of rotational symmetry of 2. It looks exactly the same after a 180° turn, so it fits onto itself twice during one full 360° turn. Dividing 360° by its angle of rotation of 180° also gives an order of 2.
A regular hexagon has an order of rotational symmetry of 6. It fits onto itself 6 times during one full 360° turn. Using the formula, 360° divided by 6 gives an angle of rotation of 60°. This is the smallest turn that maps the hexagon onto itself.
Yes, a shape can have no rotational symmetry. Some shapes only look the same after a complete 360° turn. The parking sign is one example. Rotating it by any angle less than 360° changes how it looks, so it has no rotational symmetry.