ASA Congruence

Theorem: If two pairs of angles of two triangles are equal in measurement, and the included sides are equal in length, then the triangles are congruent.

Prerequisites:
Unique ASA triangle (proof)

Proof:

Let there be two triangles $\triangle ABC$ and $\triangle DEF$, such that the angles $\angle ABC = \angle DEF$, $\angle ACB = \angle DFE$ and the included sides BC $=$ EF.

Since for the given two angles and an included side, a unique triangle can be formed (see prerequisite), hence both the triangles are congruent.

Q.E.D.


Recommended:
Unique ASA triangle
SSS congruence
SAS congruence