Point symmetry

Dependencies: Parallelogram properties (opposite sides equal, diagonals bisect each other) (Parallelogram: diagonals bisect each other, F.01), Parallelogram tests (F.04, especially (d) Parallelogram: diagonals bisect each other ⇒ parallelogram).

Statement

Let $O$ be a fixed point. Central symmetry about $O$ (also called point symmetry) is the map of the plane to itself

Equivalently, $\sigma_O$ is rotation by $180^{\circ}$ about $O$. Its geometric property is: for any two points $A$ and $B$ and their images $A' = \sigma_O(A)$, $B' = \sigma_O(B)$,