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 criterion

The Side - Angle - Side (SAS) congruence criterion states that for two triangles $\triangle A_1B_1C_1$ and $\triangle A_2B_2C_2$, if $A_1B_1 = A_2B_2$, $B_1C_1=B_2C_2$ and the included angle between $A_1B_1$ and $B_1C_1$ is congruent to the included angle between $A_2B_2$ and $B_2C_2$, then the two triangles are congruent.
In $\triangle JKL$ and $\triangle MNR$, we are given that $KL\cong NR$ and $JL\cong MR$. The included angle for sides $KL$ and $JL$ in $\triangle JKL$ is $\angle L$, and the included angle for sides $NR$ and $MR$ in $\triangle MNR$ is $\angle R$.

Step2: Determine the needed angle

For $\triangle JKL\cong\triangle MNR$ by SAS, we need $\angle L\cong\angle R$.

Answer:

$\angle L\cong\angle R$