SSS, SAS, ASA, and AAS all work, so I don't see what's special about SSA.
Accepted answer
Because SSA doesn't pin down a unique triangle — it's the **ambiguous case**.
Given two sides and an angle *not* between them, the unknown side can often swing to meet the opposite side in **two different places**, producing two genuinely different triangles that satisfy the same three measurements. Since congruence criteria must force exactly one triangle, SSA doesn't qualify.
The one exception is a **right angle**: that's the **HL** (Hypotenuse-Leg) theorem. With the right angle fixed, the Pythagorean theorem determines the third side, so no ambiguity remains. HL is really SSA rescued by a right angle.
Also note **AAA** fails for a different reason: matching angles give *similar* triangles, but the size is unconstrained.