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Rotational Symmetry

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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 two times.
 

B remember

 

So, this figure has rotational symmetry of order 2.

 

Even if a figure has no rotational symmetry, the order of rotational symmetry will still be 1 as every figure 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.