Question

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

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.

Step2: Identify given parts

We are given that $\angle J\cong\angle M$ and $\overline{JL}\cong\overline{MR}$. The included angles for the pairs of sides are $\angle J$ and $\angle M$. We need the other pair of sides that include these angles. For $\triangle JKL$ and $\triangle MNR$, the sides adjacent to $\angle J$ and $\angle M$ are $\overline{JK}$ and $\overline{MN}$ respectively.

Answer:

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