Question

what additional piece of information would you need to be able to state that △klm≅△mnk by the sss congruence theorem? (1 point)
○ (overline{km}congoverline{kn})
○ (overline{nl}congoverline{km})
○ (overline{kl}congoverline{mn})
○ (overline{kl}congoverline{lm})

Explanation:

Step1: Recall SSS Congruence Theorem

The SSS (Side - Side - Side) Congruence Theorem states that if three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent. In \(\triangle KLM\) and \(\triangle MNK\), we already know some side - relationships from the figure. We need to match the remaining sides.

Step2: Analyze the given sides

For \(\triangle KLM\) and \(\triangle MNK\), we know that the common side is \(KM\). We need to make sure that the other two pairs of sides are congruent. Looking at the options, for \(\triangle KLM\) and \(\triangle MNK\) to be congruent by SSS, we need \(\overline{KL}\cong\overline{MN}\) and \(\overline{LM}\cong\overline{NK}\). Among the given options, the correct one for the missing side - congruence to apply SSS is \(\overline{KL}\cong\overline{MN}\).

Answer:

\(\overline{KL}\cong\overline{MN}\) (the option that says \(\overline{KL}\cong\overline{MN}\))