# AAS Congruence (Angle-Angle-Side Congruence)

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

## Theorem

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

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*.