Question

in the diagram below, $overline{wx}congoverline{zy}$. which additional piece of information is required to conclude that $\triangle wyz$ and $\triangle ywx$ are congruent by side - side - side triangle congruence? $overline{wz}congoverline{xy}$ $wz>xy$ $mangle z < 90^{circ}$ $angle x$ is a right angle

Explanation:

Step1: Recall SSS congruence

For $\triangle WYZ$ and $\triangle YWX$ to be congruent by Side - Side - Side (SSS), all three pairs of corresponding sides must be congruent. We already know that $\overline{WX}\cong\overline{ZY}$. The common side for both triangles is $\overline{WY}\cong\overline{WY}$ (reflexive property). We need the third pair of sides to be congruent.

Step2: Identify the third - side pair

The third pair of corresponding sides for $\triangle WYZ$ and $\triangle YWX$ are $\overline{WZ}$ and $\overline{XY}$. For SSS congruence, we need $\overline{WZ}\cong\overline{XY}$.

Answer:

$\overline{WZ}\cong\overline{XY}$