Question

in the diagram, $overline{kl} cong overline{nr}$ and $overline{jl} cong overline{mr}$. what additional information is needed to show $\triangle jkl cong \triangle mnr$ by sas?

• $angle j cong angle m$
• $angle l cong angle r$
• $angle k cong angle n$
• $angle r cong angle k$

Explanation:

To prove \(\triangle JKL \cong \triangle MNR\) by SAS (Side - Angle - Side) congruence criterion, we need two sides and the included angle of one triangle to be congruent to the corresponding two sides and the included angle of the other triangle. We know that \(\overline{KL}\cong\overline{NR}\) and \(\overline{JL}\cong\overline{MR}\). The included angle between \(\overline{KL}\) and \(\overline{JL}\) in \(\triangle JKL\) is \(\angle L\), and the included angle between \(\overline{NR}\) and \(\overline{MR}\) in \(\triangle MNR\) is \(\angle R\). So, we need \(\angle L\cong\angle R\) to apply the SAS criterion.

Answer:

\(\boldsymbol{\angle L\cong\angle R}\)