Rotational Symmetry Order

Rotational symmetry order

The order of rotational symmetry tells you how many times a shape matches itself during one full turn of 360°. If a shape looks the same after being turned some amount, count every matching position including the starting one.

Method

1. Identify the full turn: A complete rotation is 360°.

2. Find repeated matching positions: Turn the shape until it fits exactly onto itself.

3. Count the matches: The number of times it coincides with its original position is the order.

4. Use the angle if needed: If the shape matches every equal turn, then

   order = 360° ÷ smallest angle of rotation

Examples of what to look for

• A shape that only matches after a full turn has order 1.
• A shape that matches four times in one full turn has order 4.

Check your answer

Make sure the order is a whole number and that it makes sense for the shape’s appearance. If you are given an angle, check that multiplying the order by that angle gives 360°.

Final tip

Count carefully and simplify your final answer if the exercise gives a calculation. The order must describe all identical positions in one full rotation.