Use the image to answer the question.

Question

An illustration shows a horizontal parallelogram divided into two triangles.

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

(1 point)
Responses

KM¯¯¯¯¯¯¯¯¯¯≅KN¯¯¯¯¯¯¯¯¯
Modifying above upper K upper M with bar congruent to Modifying above upper K upper N with bar

KL¯¯¯¯¯¯¯¯≅MN¯¯¯¯¯¯¯¯¯¯
Modifying above upper K upper L with bar congruent to Modifying above upper M upper N with bar

NL¯¯¯¯¯¯¯¯≅KM¯¯¯¯¯¯¯¯¯¯
Modifying above upper N upper L with bar congruent to Modifying above upper K upper M with bar

KL¯¯¯¯¯¯¯¯≅LM¯¯¯¯¯¯¯¯¯
Modifying above upper K upper L with bar congruent to Modifying above upper L upper M with bar

Answer 1

To use the SSS (Side-Side-Side) Congruence Theorem to prove that triangles \( \triangle KLM \) and \( \triangle MNK \) are congruent, you need to show that all three corresponding sides of the triangles are equal in length.

The question asks for what additional piece of information would be needed to establish this congruence. Among the options provided:

1. \( \overline{KM} \cong \overline{KN} \)
2. \( \overline{KL} \cong \overline{MN} \)
3. \( \overline{NL} \cong \overline{KM} \)
4. \( \overline{KL} \cong \overline{LM} \)

To specifically use the SSS theorem effectively, you would need to know the length of one of the sides that connects these two triangles.

Option 1, stating \( \overline{KM} \cong \overline{KN} \), provides the necessary information related to the sides of triangles \( KLM \) and \( MNK \) to verify the SSS condition.

Thus, the additional piece of information needed is:

\( \overline{KM} \cong \overline{KN} \).