Question

which theorem is not a valid theorem to show that two triangles are congruent?
a. sas triangle congruence theorem
b. ssa triangle congruence theorem
c. asa triangle congruence theorem
d. aas triangle congruence theorem

Explanation:

To determine the invalid triangle congruence theorem, we analyze each option:

• Option A (SAS): Side - Angle - Side is a valid congruence theorem. If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent.
• Option B (SSA): Side - Side - Angle is not a valid congruence theorem. Given two sides and a non - included angle, there can be two different triangles (the ambiguous case in the Law of Sines), so we cannot guarantee the congruence of two triangles using SSA.
• Option C (ASA): Angle - Side - Angle is a valid congruence theorem. If two angles and the included side of one triangle are equal to two angles and the included side of another triangle, the triangles are congruent.
• Option D (AAS): Angle - Angle - Side is a valid congruence theorem. If two angles and a non - included side of one triangle are equal to two angles and the corresponding non - included side of another triangle, the triangles are congruent.

Answer:

B. SSA Triangle Congruence Theorem