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?
$\bigcirc angle j cong angle m$
$\bigcirc angle l cong angle r$
$\bigcirc angle k cong angle n$
$\bigcirc angle r cong angle k$

Explanation:

Step1: Recall SAS congruence rule

SAS (Side-Angle-Side) requires two pairs of congruent sides, with the included angle between them being congruent.

Step2: Identify given congruent sides

Given $\overline{KL} \cong \overline{NR}$ and $\overline{JL} \cong \overline{MR}$.

Step3: Locate included angles

For $\triangle JKL$, the angle between $\overline{KL}$ and $\overline{JL}$ is $\angle L$. For $\triangle MNR$, the angle between $\overline{NR}$ and $\overline{MR}$ is $\angle R$.

Step4: Match required included angle

To satisfy SAS, the included angles $\angle L$ and $\angle R$ must be congruent.

Answer:

$\boldsymbol{\angle L \cong \angle R}$