Question

in the diagram, \\( \overline { k l } \cong \overline { n r } \\) and \\( \overline { j l } \cong \overline { m r } \\). what additional information is needed to show \\( \triangle j k l \cong \triangle m n r \\) by sas?
\\( \angle k \cong \angle n \\)
\\( \angle r \cong \angle k \\)
\\( \angle l \cong \angle r \\)
\\( \angle j \cong \angle m \\)

Explanation:

Step1: Recall the SAS (Side - Angle - Side) congruence criterion

The 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 are given that \(KL\cong NR\) and \(JL\cong MR\).

Step2: Identify the included angles

For \(\triangle JKL\) and \(\triangle MNR\), the sides \(KL\) and \(JL\) in \(\triangle JKL\) have an included angle \(\angle L\). The sides \(NR\) and \(MR\) in \(\triangle MNR\) have an included angle \(\angle R\).

Answer:

\(\angle L\cong\angle R\)