Definition:Symmetry Mapping

Definition
A symmetry mapping (or just symmetry) of a geometric figure is a bijection from the figure to itself which preserves the distance between points.

In other words, it is a self-congruence.

Intuitively, a symmetry is a movement of the figure so that it looks exactly the same after it has been moved.

Linguistic Note
The word symmetry comes from Greek συμμετρεῖν (symmetría) meaning measure together.