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Question

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

(1 point)
Responses

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

Yes, △ABC ≅ △MLN
by the SSS Congruence Theorem.
Yes, △ABC ≅ △MLN
by the SSS Congruence Theorem.

Yes, △ABC ≅ △MNL
by the SSS Congruence Theorem.
Yes, △ABC ≅ △MNL
by the SSS Congruence Theorem.

No

1 answer

To determine if the triangles are congruent using the SSS (Side-Side-Side) Congruence Theorem, we need to establish that all three corresponding sides of the triangles are equal in length.

If you are provided with specific side lengths for triangles ABC and LMN (or whichever letters are used in your case), you would compare the lengths as follows:

  1. Confirm that \( AB = LM \)
  2. Confirm that \( BC = MN \)
  3. Confirm that \( CA = NL \)

If all three pairs of sides are equal in length, you can conclude that the triangles are congruent.

If the triangles are congruent, you would write the congruence statement accordingly. For example:

  • If \( ABC \) corresponds to \( LMN \), then the statement would be: Yes, \( △ABC ≅ △LMN \) by the SSS Congruence Theorem.

Make sure to choose the correct corresponding letters based on the problem context.

In the provided options, the first response is likely correct, but it depends on the actual side lengths given in your problem.