Triangles J K L and M N R are shown.

Question

In the diagram, ∠J ≅ ∠M and JL ≅ MR. What additional information is needed to show ΔJKL ≅ △MNR by SAS?

KL ≅ NR
∠L ≅ ∠R
∠K ≅ ∠N
JK ≅ MN

Answer 1

To show that ΔJKL ≅ ΔMNR by the Side-Angle-Side (SAS) congruence criterion, you need to establish that two sides and the included angle of one triangle are congruent to two sides and the included angle of the other triangle.

You are given that ∠J ≅ ∠M (the included angles) and JL ≅ MR (one pair of corresponding sides). The additional information needed should complete the SAS condition. Among the options you listed, the correct choice to satisfy the SAS criterion is:

JK ≅ MN

This means you would have:

• Side JL ≅ MR
• Angle ∠J ≅ ∠M
• Side JK ≅ MN

This confirms the SAS congruence criterion, which allows you to conclude that ΔJKL ≅ ΔMNR.