Question

in the diagram, ∠j ≅ ∠m and jl ≅ mr. what additional information is needed to show △jkl ≅ △mnr by sas?
○ kl ≅ nr
○ ∠l ≅ ∠r
○ ∠k ≅ ∠n
○ jk ≅ mn

Explanation:

Step1: Recall SAS congruence criterion

The Side - Angle - Side (SAS) 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.
We know that $\angle J\cong\angle M$ and $\overline{JL}\cong\overline{MR}$. The included angles for the pairs of sides are $\angle J$ for $\overline{JK}$ and $\overline{JL}$, and $\angle M$ for $\overline{MN}$ and $\overline{MR}$.

Step2: Identify the needed side

For $\triangle{JKL}\cong\triangle{MNR}$ by SAS, we need the side adjacent to the given equal angles to be congruent. That is, we need $\overline{JK}\cong\overline{MN}$.

Answer:

$\overline{JK}\cong\overline{MN}$