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Rotational Symmetry

A figure has rotational symmetry if it can be rotated about a point less than a full turn and look the same as it did before the rotation.

The order of rotational symmetry is the number of times a figure looks the same as it did originally when it is rotated through 360°.


For example: Consider this figure.

D remember


If we rotate it one-half turn, it will look the same.

A remember


So, it has rotational symmetry.


Also, observe that when the figure is rotated through 360°, it looks the same three times.

B remember


So, this figure has rotational symmetry of order 3.


Even if a figure has no rotational symmetry, the order of rotational symmetry will still be 1 as every shape looks the same at the end of a complete rotation (360°).


For example: Consider this figure.

C remember


The order of rotational symmetry of this figure is 1.

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