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Triangle Congruence
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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 ΔABC are PM ¯ , NQ ¯ , and RS ¯ .

Perpendicular bisectors have special properties. These properties can be proven by applying right triangle congruence theorems.