Question

in the diagram, ( overline{kl} cong overline{rq} ).
what additional information is needed to prove ( \triangle jkl cong \triangle prq ) by asa?
enter your answers in the boxes.
( angle 2 cong angle square ) and ( angle square cong angle square )

Explanation:

Step1: Recall ASA (Angle - Side - Angle) congruence criterion

ASA states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent. We know that \( \overline{KL}\cong\overline{RQ}\).

Step2: Identify the angles

For \( \triangle JKL\) and \( \triangle PRQ\), if we consider the side \( \overline{KL}\) (in \( \triangle JKL\)) and \( \overline{RQ}\) (in \( \triangle PRQ\)) as the included sides.
We already have \( \overline{KL}\cong\overline{RQ}\). For ASA, we need two pairs of angles.
We know that \( \angle2\) (in \( \triangle JKL\)) should be congruent to \( \angle4\) (in \( \triangle PRQ\)) and \( \angle3\) (in \( \triangle JKL\)) should be congruent to \( \angle6\) (in \( \triangle PRQ\))

Answer:

\(\angle2\cong\angle4\) and \(\angle3\cong\angle6\)