The SSS Congruence Theorem Quick Check

Question

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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)
Responses

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

KL¯¯¯¯¯¯¯¯≅LM¯¯¯¯¯¯¯¯¯
Modifying above upper K upper L with bar congruent to Modifying above upper L upper M with bar
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Answer 1

To apply the SSS Congruence Theorem, which states that two triangles are congruent if all three corresponding sides are equal in length, you need to know all three sides of the triangles.

In this case, if you already have two sides from the respective triangles (for example, KL and MN), you would need to know a corresponding third pair of sides to confirm the congruence.

The most relevant response would typically be one of the pairs that represent the third side in each triangle. For the triangles △KLM and △MNK, you would likely need to establish that one additional pair of sides is equal, specifically a side that forms the base for both triangles.

Among the options, the most appropriate choice would likely be:

NL ≅ KM

This confirms the necessary additional side for the SSS theorem when you already have two others established. Adjust your selection based on the sides you've already confirmed to be equal in the figure.