To show that triangles \( \Delta JKL \) and \( \Delta MNR \) are congruent by the Side-Angle-Side (SAS) postulate, we already have the following information:
- \( KL \cong NR \) (one pair of corresponding sides)
- \( JL \cong MR \) (another pair of corresponding sides)
To apply the SAS postulate, we need to show that the included angles between these sides are congruent. That is, we need to find a congruence statement for the angles at the vertices \( J \) and \( M \) or \( K \) and \( N \) or \( L \) and \( R \).
If we consider the angles, we can look at the choices given:
- \( \angle J \cong \angle M \)
- \( \angle L \cong \angle R \)
- \( \angle K \cong \angle N \)
- \( \angle R \cong \angle K \)
Any of these pairs would provide the necessary angle for SAS if they are included angles between the sides JL and KL, and MR and NR.
However, the most direct pair that fits into the SAS criterion, considering we’ve already established the corresponding sides, would be:
\( \angle K \cong \angle N \).
We need to show that the angle between sides \( JL \) (congruent to \( MR \)) and \( KL \) (congruent to \( NR \)) is congruent, thus fulfilling the requirement needed for SAS.
So, the additional information needed to show \( \Delta JKL \cong \Delta MNR \) by SAS is:
\( \angle K \cong \angle N \).
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