AAS Congruence (Angle-Angle-Side Congruence)

AAS Congruence (Angle-Angle-Side Congruence)

How to solve AAS congruence problems: theorem, example and its solution (proof)."

Theorem

ASA Congruence: If two angles and the non-included side of a triangle are congruent to two angles and the non-included side of another triangle, then those two triangles are congruent.

If two angles and the non-included side of a triangle
are congruent to
two angles and the non-included side of another triangle,
then those two triangles are congruent.

Example

Given: line segment AB is congruent to line segment AD, angle PAB is congruent to angle PCD. Prove: triangle PAB is congruent to triangle PCD.

Start from the given statements.

Two column proof

APB and ∠CPD are vertical angles.
So m∠APB ≅ m∠CPD.

Two angles and the non-included side of △PAB
are congruent to
two angles and the non-included side of △PCD.

Then, by the AAS congruence theorem,
PAB ≅ △PCD.