Question

in the diagram, $overline{kl}congoverline{nr}$ and $overline{jl}congoverline{mr}$. what additional information is needed to show $\triangle{jkl}cong\triangle{mnr}$ by sas?
$angle{j}congangle{m}$
$angle{l}congangle{r}$
$angle{k}congangle{n}$
$angle{r}congangle{k}$

Explanation:

Step1: Recall SAS congruence criterion

SAS (Side - Angle - Side) requires two pairs of corresponding sides to be congruent and the included angles between those sides to be congruent. Given $KL\cong NR$ and $JL\cong MR$, the included angles for these pairs of sides are $\angle L$ and $\angle R$ respectively.

Step2: Determine the needed information

To prove $\triangle{JKL}\cong\triangle{MNR}$ by SAS, we need $\angle L\cong\angle R$.

Answer:

$\angle L\cong\angle R$