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

SAS (Side - Angle - Side) congruence criterion states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

Step2: Identify given sides

We are given that $\overline{KL}\cong\overline{NR}$ and $\overline{JL}\cong\overline{MR}$. The included angle for sides $\overline{KL}$ and $\overline{JL}$ in $\triangle{JKL}$ is $\angle{L}$, and the included angle for sides $\overline{NR}$ and $\overline{MR}$ in $\triangle{MNR}$ is $\angle{R}$.

Step3: Determine needed angle

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

Answer:

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