SSS Congruence

Theorem: If all the three pairs of sides of two triangles are equal in length, then the triangles are congruent.

Prerequisites:
Unique SSS 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 CA $=$ FD $= l_3$.

Since for the given three side lengths a unique triangle can be formed (see prerequisite), hence both the triangles are congruent.

Q.E.D.


Recommended:
SSS similarity
ASA congruence
RHS congruence