# AAS Congruence (Angle-Angle-Side Congruence)

How to prove the congruence of triangles by using the AAS congruence theorem: theorem, example, and its solution.

## Theorem

For two triangles,

if two angles and a non-included side of each triangle

are congruent,

then those two triangles are congruent.

This is the AAS congruence theorem.

## Example

Start from the given statement.*AB* ≅ *CD*

Two-column proof

Use the other given statement.

∠*PAB* ≅ ∠*PCD*

∠*APB* and ∠*CPD* are vertical angles.

Vertical angles are congruent.

So ∠*APB* ≅ ∠*CPD*.

Vertical angles (Opposite angles)

For △*PAB* and △*PCD*,

two angles and a non-included side of each triangle

are congruent.

Then, by the AAS congruence theorem,

△*PAB* and △*PCD* are congruent.

So this is the two-column proof of the example.