What additional piece of information would you need to be able to state that △KLM≅△MNK by the SSS Congruence Theorem? (1 point)

Question

KL¯¯¯≅LM¯¯¯
KM¯¯¯≅KN¯
KL¯¯¯¯≅MN¯¯¯¯
NL¯¯¯¯≅KM¯¯¯¯

Answer 1

To use the Side-Side-Side (SSS) Congruence Theorem to state that triangles \( \triangle KLM \) is congruent to \( \triangle MNK \), we need to show that all three pairs of corresponding sides of the two triangles are equal in length.

From the information provided, we have:

1. \( KL \cong LM \)
2. \( KM \cong KN \)
3. \( KL \cong MN \)

To fully establish the congruence of the triangles through the SSS congruence theorem, we need to establish one additional pair of corresponding sides.

The most useful additional piece of information would be:

\( LM \cong KN \)

With this piece of information, we would then have all three pairs of sides of the triangles \( KLM \) and \( MNK \) congruent, allowing us to conclude that \( \triangle KLM \cong \triangle MNK \) by the SSS Congruence Theorem.