EXAMPLE 1 OF TRIANGLE CONGRUENCY PROOF (AAS)
To prove triangles ADB and AEB are congruent, given that triangle ABC is isosceles (AC=BC).
∠EAB=∠DBA (equal angles in isosceles triangle ABC).
∠ADB=∠AEB (angles in the same segment of a circle).
side AB is common to both triangles.
So we have two angles and one side congruent (AAS) therefore triangles ADB and AEB are congruent.
EXAMPLE 2 OF TRIANGLE CONGRUENCY PROOF (AAS)
To prove that triangles QRS and QPS are congruent, given that ∠PQS=∠RQS, ∠QSP=∠QSR. Hence prove that QR and QP have the same length.
There are a pair of given congruent angles. The side is QS is common to both triangles, so the triangles are congruent (AAS—two angles and a side). Therefore sides QR and QP are congruent, that is, they have the same length.