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 the SAS (Side - Angle - Side) congruence criterion

For two triangles \(\triangle ABC\) and \(\triangle DEF\), \(\triangle ABC\cong\triangle DEF\) by SAS if \(AB = DE\), \(\angle A=\angle D\), and \(AC = DF\) (the angle is included between the two sides).

Step2: Analyze the given information for \(\triangle JKL\) and \(\triangle MNR\)

We are given that \(\angle J\cong\angle M\) and \(\overline{JL}\cong\overline{MR}\). To use the SAS criterion, we need the sides adjacent to the given angles to be congruent.

In \(\triangle JKL\), the sides adjacent to \(\angle J\) are \(\overline{JK}\) and \(\overline{JL}\). In \(\triangle MNR\), the sides adjacent to \(\angle M\) are \(\overline{MN}\) and \(\overline{MR}\).

Since \(\overline{JL}\cong\overline{MR}\) and \(\angle J\cong\angle M\), we need \(\overline{JK}\cong\overline{MN}\)

Answer:

\(\overline{JK}\cong\overline{MN}\) (the fourth option)