traingal thoram aas proof

Question

Aas thoram in easy way

Answer 1

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.