Triangle Congruence Proofs

AAS Congruence states that if two angles and the non-included side of one triangle are congruent to two angles and the non-included side of another triangle, then the triangles are congruent.

SSS Congruence states that if three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.

SAS Congruence states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.

ASA Congruence states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.

HL Congruence applies to right triangles and states that if the hypotenuse and one leg of one right triangle are congruent to the hypotenuse and one leg of another right triangle, then the triangles are congruent.

CPCTC stands for 'Corresponding Parts of Congruent Triangles are Congruent', which is used after proving triangles are congruent to show that their corresponding parts are also congruent.

Congruence means that two figures have the same shape and size, or that they can be made to coincide by rigid motions.

A midpoint is a point that divides a line segment into two equal parts.

Perpendicular lines are lines that intersect at a right angle (90 degrees).

Right angles are angles that measure exactly 90 degrees.