Question

the sss congruence theorem quick check
use the image to answer the question.
what additional piece of information would you need to be able to state that △klm≅△mnk by the sss congruence theorem?
(1 point)
○nl≅km
○km≅kn
○kl≅lm
○kl≅mn

Explanation:

Step1: Recall SSS Congruence Theorem

The SSS (Side - Side - Side) Congruence Theorem states that if the three sides of one triangle are congruent to the three sides of another triangle, then the two triangles are congruent.

Step2: Identify given congruent sides

In \(\triangle KLM\) and \(\triangle MNK\), from the figure, we can see that \(KM = KM\) (common side) and one pair of sides is already marked as congruent. We need the third - pair of corresponding sides to be congruent.

Step3: Determine the missing side - congruence

For \(\triangle KLM\cong\triangle MNK\) by SSS, we need \(\overline{KL}\cong\overline{MN}\) since these are the remaining non - congruent corresponding sides.

Answer:

\(\overline{KL}\cong\overline{MN}\)