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 sides in the SAS criterion are the angles between the two sides. For \(\triangle JKL\) and \(\triangle MNR\), the sides around the angles \(\angle J\) and \(\angle M\) are considered.

Step2: Identify the required side

We already have one side \(\overline{JL}\cong\overline{MR}\) and the angle \(\angle J\cong\angle M\). We need the other side around \(\angle J\) in \(\triangle JKL\) and the other side around \(\angle M\) in \(\triangle MNR\) to be congruent. The side around \(\angle J\) in \(\triangle JKL\) is \(\overline{JK}\) and the side around \(\angle M\) in \(\triangle MNR\) is \(\overline{MN}\). So we need \(\overline{JK}\cong\overline{MN}\).

Answer:

D. \(\overline{JK}\cong\overline{MN}\)