# AAS Congruence

How to use the AAS congruence to show that the given triangles are congruent: theorem, 1 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.

(Angle-Angle-Side congruence)

## Example

To write a two-column proof,

make a two-column form like this.

Start from the given statement:

AB ≅ CD.

Use the other given statement:

∠PAB ≅ ∠PCD.

∠APB and ∠CPD are vertical angles.

Vertical angles are congruent.

So ∠APB ≅ ∠CPD.

For △PAB and △PCD,

two angles and a non-included side of each triangle

are congruent.

∠APB ≅ ∠CPD

∠PAB ≅ ∠PCD

AB ≅ CD

Then, by the AAS congruence theorem,

△PAB and △PCD are congruent.

You found the Prove statement

△PAB ≅ △PCD.

So close the two-column form

by drawing the bottom line.

This is the proof of the example.