Answer: JK ≅ MN
WORKINGS
Given,
Angle J is congruent to Angle M (∠J ≅ ∠M)
Side JL is congruent to side MR (JL ≅ MR)
Triangle JKL is congruent to Triangle MNR ΔJKL ≅ △MNR
We are to give the additional information to show that triangle JKL is congruent to triangle MNR by SAS Postulate; SAS Postulate states that if two sides of one triangle and the angle formed by them are congruent to the corresponding parts of another triangle, then the two triangles are congruent.
Angle J is formed by sides JL and JK
Angle M is formed by sides MR and MN
Therefore, If the two triangles are congruent,
Angle J is congruent to Angle M
and Side JL is congruent to side MR
Then, Side JK is congruent to side MN (JK ≅ MN).
The additional information is needed to show ΔJKL ≅ △MNR by SAS is JK ≅ MN