Reflection: axis ⊥ bisects each pair of corresponding points

Depends on: Perpendicular bisector ⇔ equidistant from endpoints, SSS congruence.

Statement

Let $\ell$ be a line in the plane, and denote by $\sigma_\ell$ the reflection across $\ell$: each point $P$ maps to $P' = \sigma_\ell(P)$ such that $\ell$ is the perpendicular bisector of segment $PP'$ — this is the geometric definition of reflection.

Then $\sigma_\ell$ preserves distances and angles: for any pair of points $A$, $B$ and their images $A' = \sigma_\ell(A)$, $B' = \sigma_\ell(B)$,

In other words, reflection is a congruence transformation — it carries each figure as a whole to the other side of $\ell$, preserving lengths and angles.