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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

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

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.

Yes, △ABC≅△NLM by the SSA Congruence Theorem.
Yes, triangle upper A upper B upper C congruent to triangle upper N upper L upper M by the SSA Congruence Theorem.
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Answer 1

The correct response is:

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

However, note that the SSA (Side-Side-Angle) criterion does not actually guarantee triangle congruence in general. It can lead to the ambiguous case where two different triangles can satisfy the given conditions. For two triangles to be definitively congruent, we would typically rely on criteria such as SSS (Side-Side-Side), SAS (Side-Angle-Side), or ASA (Angle-Side-Angle). Given that these triangles are described as being congruent, we would expect a more reliable congruence statement or matching criteria, rather than relying on SSA.

If you have specific measurements or angles, you would need to confirm that they match to conclude definitively that the triangles are congruent.

In the absence of additional information, use of the SSA criterion is not strictly correct.