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
○ kl≅lm
○ kl≅mn
○ km≅kn

Explanation:

Step1: Recall SSS congruence theorem

SSS states that if three sides of one triangle are congruent to three sides of another triangle, the triangles are congruent.

Step2: Analyze given sides

In $\triangle KLM$ and $\triangle MNK$, we can see from the figure that $\overline{KM}$ is common. Also, assume one - pair of sides are already marked as congruent (the single - hash marks on $\overline{LN}$ and $\overline{KM}$). For $\triangle KLM\cong\triangle MNK$ by SSS, we need $\overline{KL}\cong\overline{MN}$ and $\overline{LM}\cong\overline{NK}$ (the latter might be given or marked in a different way not shown in the problem - setup, but the missing piece for the options given is $\overline{KL}\cong\overline{MN}$).

Answer:

C. $\overline{KL}\cong\overline{MN}$