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Question

Two congruent triangles in different orientations, one next to the other. Triangle A B C is on the left, and triangle L M N is on the right.

Are the triangles congruent? If so, write a congruence statement and reason why.

(1 point)
Responses

Yes, △ABC≅△LMN by the SSA Congruence Theorem.
Yes, triangle upper A upper B upper C congruent to triangle upper L upper M upper N by the SSA Congruence Theorem.

Yes, △ABC≅△MLN by the SSA Congruence Theorem.
Yes, triangle upper A upper B upper C congruent to triangle upper M upper L upper N by the SSA Congruence Theorem.

No, the triangles are not necessarily congruent.
No, the triangles are not necessarily congruent.

Yes, △ABC≅△NLM by the SSA Congruence Theorem.

Answer 1

The correct response is:

No, the triangles are not necessarily congruent.

The SSA (Side-Side-Angle) condition does not guarantee the congruence of triangles. The congruence of triangles can be established using the SSS (Side-Side-Side), SAS (Side-Angle-Side), or AAS (Angle-Angle-Side) theorems, but SSA can result in the ambiguous case where two different triangles could satisfy the given side lengths and angle conditions. Therefore, the triangles are not guaranteed to be congruent based on the information given.