Question

Use the image to answer the 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)ResponsesKL¯¯¯¯¯¯¯¯≅LM¯¯¯¯¯¯¯¯¯Modifying above upper K upper L with bar congruent to Modifying above upper L upper M with barKM¯¯¯¯¯¯¯¯¯¯≅KN¯¯¯¯¯¯¯¯¯Modifying above upper K upper M with bar congruent to Modifying above upper K upper N with barKL¯¯¯¯¯¯¯¯≅MN¯¯¯¯¯¯¯¯¯¯Modifying above upper K upper L with bar congruent to Modifying above upper M upper N with barNL¯¯¯¯¯¯¯¯≅KM¯¯¯¯¯¯¯¯¯¯

Answer 1

To determine that triangles \( \triangle KLM \) and \( \triangle MNK \) are congruent by the SSS (Side-Side-Side) Congruence Theorem, you need to establish that all three pairs of corresponding sides of the triangles are congruent.

Given what you need, one crucial piece of information would be:

The length of side \( LM \) is equal to the length of side \( NK \).

This additional information (congruence of the sides \( LM \) and \( NK \)) would allow you to state that \( \triangle KLM \cong \triangle MNK \) by SSS, provided that the other corresponding sides are already established as congruent (i.e., \( KL \equiv MN \) and \( KM \equiv KN \)).