Question

triangle congruence: sas
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 l \cong \angle r \\)
\\( \angle r \cong \angle k \\)
\\( \angle j \cong \angle m \\)
\\( \angle k \cong \angle n \\)

Explanation:

Step1: Recall SAS Congruence Rule

The Side - Angle - Side (SAS) congruence rule 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 \( \overline{KL}\cong\overline{NR}\) and \( \overline{JL}\cong\overline{MR}\). The included angles for these sides in \( \triangle JKL\) and \( \triangle MNR\) are \( \angle L\) and \( \angle R\) respectively.

Step2: Apply SAS Rule

For \( \triangle JKL\cong\triangle MNR\) by SAS, we need the included angles to be congruent. So we need \( \angle L\cong\angle R\)

Answer:

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