SAS Congruence

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

Prerequisites:
Unique SAS triangle (proof)

Proof:

Let there be two triangles $\triangle ABC$ and $\triangle DEF$, such that the sides AB $=$ DE $= l_1$, BC $=$ EF $= l_2$, and the included angles $\angle ABC = \angle DEF$.

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

Q.E.D.


Recommended:
Unique SAS triangle
SSS congruence
ASA congruence