Question

1. what additional information is needed to prove the triangles are congruent by the sas postulate?

∠yxw ≅ ∠yzw
wy ≅ xz
∠xwy ≅ ∠zwy
wy ⊥ xz

Explanation:

Step1: Recall the SAS (Side - Angle - Side) Postulate

The SAS postulate 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.
In triangles \( \triangle XWY\) and \( \triangle ZWY\), we already know that \( WX\cong WZ\) (given by the marks on the sides). Also, \( WY\) is a common side, so \( WY\cong WY\).

Step2: Identify the included angle

For the SAS postulate, we need the included angle between the two sides. The sides \( WX\) and \( WY\) in \( \triangle XWY\) and \( WZ\) and \( WY\) in \( \triangle ZWY\) have the included angles \( \angle XWY\) and \( \angle ZWY\) respectively.

Answer:

\(\angle XWY\cong\angle ZWY\) (the third option)