How to use the AAS congruence to show that the given triangles are congruent: theorem, 1 example, and its solution.
For two triangles,
if two angles and a non-included side of each triangle
then those two triangles are congruent.
This is the AAS congruence theorem.
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
∠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.