1. The problem asks which theorem is NOT valid to prove that two triangles are congruent. 2. The common triangle congruence theorems are: - SAS (Side-Angle-Side): Two sides and the included angle are equal. - ASA (Angle-Side-Angle): Two angles and the included side are equal. - AAS (Angle-Angle-Side): Two angles and a non-included side are equal. - SSA (Side-Side-Angle): Two sides and a non-included angle are equal. 3. Important rule: SSA is generally NOT a valid congruence theorem because it can produce ambiguous cases where two different triangles satisfy the same SSA conditions. 4. Therefore, the invalid theorem to show triangle congruence is SSA. Final answer: B. SSA Triangle Congruence Theorem