Question

in the diagram. \\( \angle q \cong \angle x \\).

what additional information is needed to prove \\( \triangle qrs \cong \triangle xyz \\) by sas?

enter your answers in the boxes.

side \\( r \cong \\) side \\( \square \\) and side \\( s \cong \\) side \\( \square \\)

Explanation:

Step1: Recall SAS congruence rule

The SAS (Side - Angle - Side) 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.

Step2: Identify the included angle and corresponding sides

We are given that \(\angle Q\cong\angle X\). For \(\triangle QRS\) and \(\triangle XYZ\), the sides adjacent to \(\angle Q\) are \(r\) and \(s\), and the sides adjacent to \(\angle X\) are \(z\) and \(y\).

Answer:

side \(r\cong\) side \(z\) and side \(s\cong\) side \(y\)