Question

What additional piece of information would you need to be able to state that △KLM≅△MNK by the SSS Congruence Theorem? (1 point) Responses KL¯¯¯¯¯¯¯¯≅LM¯¯¯¯¯¯¯¯¯ Modifying above upper K upper L with bar congruent to Modifying above upper L upper M with bar KL¯¯¯¯¯¯¯¯≅MN¯¯¯¯¯¯¯¯¯¯ Modifying above upper K upper L with bar congruent to Modifying above upper M upper N with bar KM¯¯¯¯¯¯¯¯¯¯≅KN¯¯¯¯¯¯¯¯¯ Modifying above upper K upper M with bar congruent to Modifying above upper K upper N with bar NL¯¯¯¯¯¯¯¯≅KM¯¯¯¯¯¯¯¯¯¯

Answer 1

To state that △KLM ≅ △MNK by the SSS (Side-Side-Side) Congruence Theorem, you need to show that all three corresponding sides of the triangles are congruent.

You already have some congruences stated among the sides, but the missing information for the SSS theorem will depend on which pair of sides is currently not stated as congruent.

From your responses, the congruences are:

1. KL ≅ LM
2. KL ≅ MN
3. KM ≅ KN

The missing piece of information generally involves confirming congruence for the third pair of corresponding sides. Thus, the answer could be:

You need either:

• NL ≅ KM (the side opposite to KL if KL is matched with a side from △MNK)
• Another congruence statement for a side in a pair.

Essentially, you will need to confirm that at least one more side length (either KL, LM, KM, or KN) is congruent to its corresponding side in triangle △MNK.