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?

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

Explanation:

Step1: Recall SAS congruence rule

SAS requires two sides and included angle of one triangle ≅ corresponding parts of another.

Step2: List given congruent sides

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

Step3: Identify included angles

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

Step4: Match required angle congruence

To apply SAS, the included angles must be congruent: $\angle L \cong \angle R$.

Answer:

$\angle L \cong \angle R$ (Option: $\angle L \cong \angle R$)