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

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

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

KL¯¯¯¯¯¯¯¯≅LM¯¯¯¯¯¯¯¯¯

Answer 1

To use the SSS (Side-Side-Side) Congruence Theorem to establish that triangle \( \triangle KLM \) is congruent to triangle \( \triangle MNK \), you would need to know the lengths of all three corresponding sides of the triangles.

Given the options:

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

The most relevant piece of information that directly corresponds to the SSS Congruence Theorem is:

• \( \overline{KL} \cong \overline{MN} \)
• \( \overline{NL} \cong \overline{KM} \)
• \( \overline{KM} \cong \overline{KN} \)

Out of these, the response required most closely relates to confirming the pairs of sides that correspond to the triangles.

To fully apply SSS, you would typically need to identify any 3 sides as corresponding to one another. The most appropriate answer in this context would be:

KL¯¯¯¯¯¯¯¯≅MN¯¯¯¯¯¯¯¯¯¯

This establishes one pair of the three necessary sides for congruency. You would still need two more corresponding sides to conclude congruency using the SSS theorem.