AAS Congruence (Angle-Angle-Side Congruence)
How to prove the congruence of triangles by using the AAS congruence theorem: theorem, 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.
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.
Vertical angles (Opposite angles)
For △PAB and △PCD,
two angles and a non-included side of each triangle
Then, by the AAS congruence theorem,
△PAB and △PCD are congruent.
So this is the two-column proof of the example.