The SSA condition (Side-Side-Angle) which specifies two sides and a non-included angle (also known as ASS (Angle-Side-Side)) does not always prove congruence.

Specifically, SSA does not prove congruence when the angle is acute and the opposite side is shorter or equal to the adjacent side but longer than the sine of the angle times the adjacent side. This is the ambiguous case. In all other cases, SSA proves congruence. Notice that the opposite side cannot be smaller than the adjacent side times the sine of the angle as this could not describe a triangle.

The SSA condition proves congruence if the angle is obtuse or right. In the case of the right angle (also known as the HL (Hypotenuse-Leg) condition), we can calculate the third side and fall back on SSS.

The SSA condition proves congruence if the angle is acute and the opposite side either equals the adjacent side times the sine of the angle (right triangle) or is longer than the adjacent side.

SAS, SSS, ASA, एवं AAS
SSA: सर्वांगसमता की संदिग्ध स्थिति
त्रिभुजों की सर्वांगसमता
AAA