Answer:
[tex]\textsf{D)}\quad \overline{WY} \perp \overline{XZ}[/tex]
Step-by-step explanation:
The SAS (Side-Angle-Side) Congruence Theorem states that if two sides and the included angle in one triangle are congruent to two sides and the included angle in another triangle, then the two triangles are congruent.
Triangles XYW and ZYW share the common side WY, and the ticks on XY and YZ indicate that these line segments are congruent. Therefore, two corresponding sides are congruent in the triangles.
An included angle is the angle between the two sides that share a common vertex. Therefore, the included angle between XY and WY is WYX, and the included angle between YZ and WY is WYZ. For these angles to be congruent, they would have to be right angles, since they form a linear pair. If two lines are at right angles, they are considered perpendicular to each other.
Therefore, the additional information that is needed to prove the triangles are congruent by SAS is:
[tex]\Large\boxed{\boxed{\overline{WY} \perp \overline{XZ}}}[/tex]
