Question

1. for a \\( \triangle x y z, \angle y \cong \angle z \\). which sides must be congruent?

\\( \overline{y z} \\) and \\( \overline{x y} \\)
\\( \overline{x y} \\) and \\( \overline{x z} \\)
\\( \overline{x z} \\) and \\( \overline{y z} \\)
\\( \overline{x y}, \overline{y z} \\), and \\( \overline{x z} \\)

Explanation:

Step1: Recall the Isosceles Triangle Theorem

In a triangle, if two angles are congruent, then the sides opposite those angles are congruent.

Step2: Identify the sides opposite the congruent angles

In \(\triangle XYZ\), \(\angle Y\cong\angle Z\). The side opposite \(\angle Y\) is \(\overline{XZ}\), and the side opposite \(\angle Z\) is \(\overline{XY}\).

Answer:

\(\overline{XY}\) and \(\overline{XZ}\)