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≅△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.
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≅△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.
No, the triangles are not necessarily congruent.
No, the triangles are not necessarily congruent.
No, the triangles are not necessarily congruent.
To determine if two triangles are congruent, we can look for congruent corresponding parts (sides and angles). Two triangles are congruent if all corresponding sides and angles are congruent.
However, in the given scenario, we are only provided with one angle and two sides of the triangles. This is known as the Side-Side-Angle (SSA) condition. While the SSA condition can sometimes determine the congruence of two triangles, it is not a sufficient condition on its own. There is a possibility that two triangles could have the same side lengths and angle measurements but still not be congruent due to the possibility of different orientations.
Therefore, without additional information or congruent corresponding parts, we cannot conclude that the triangles are congruent.