Congruence in Right Triangles
Triangle congruence can be applied to geometric constructions of the perpendicular bisectors of a triangle.
Definition
A perpendicular bisector of a triangle is a line or a segment that passes through the midpoint of a side of a triangle and is perpendicular to that side.

The three perpendicular bisectors of are and
Perpendicular bisectors have special properties. These properties can be proven by applying right triangle congruence theorems.