In mathematics, a figure possessing symmetry can be subjected to certain operations which leave the whole unchanged.

The letters A and B have bilateral symmetry by vertical and horizontal reflection respectively. The letter Z is symmetrical for a rotation through 180°.

For mathematical convenience the identity operation, leaving the figure unchanged, is included in the list of symmetrical operations, so that even a completely irregular figure has this symmetry.

Symmetry can also be used in a broader sense in other branches of mathematics to describe a property that does not change under certain types of transformations. For example, the equation `x`² + `y`² = 25 could be considered symmetric with respect to `x` and `y`, since exchanging `x` and `y` in the equation produces the same equation.