AAS Congruence

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

Theorem

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

Example

Solution

To write a two-column proof,
make a two-column form like this.

Start from the given statement:
ABCD.

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
ABCD

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.