The correct answer is B) SSA.
To establish the congruence of two triangles, specific criteria, or postulates, are utilized. These include:
- ASA (Angle-Side-Angle): This postulate states that if two angles and the included side of one triangle are congruent to the corresponding two angles and the included side of another triangle, then the two triangles are congruent.
- SAS (Side-Angle-Side): This postulate indicates that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, the two triangles are congruent.
- SSS (Side-Side-Side): According to this postulate, if all three sides of one triangle are congruent to all three sides of another triangle, then the triangles are congruent.
On the other hand, SSA (Side-Side-Angle) does not guarantee congruence. Two triangles can have two sides and a non-included angle that are congruent without being congruent themselves, leading to the ambiguous case. Thus, SSA is not a valid method for proving triangle congruence, making it the correct answer to the question posed.