Question

1. tyler has proven that triangle wyz is congruent to triangle wyx using the side - side - side triangle congruence theorem. why can they now conclude that diagonal wy bisects angles zwx and zyx?

Explanation:

Step1: Recall congruence theorem

Since $\triangle WYZ\cong\triangle WYX$ by S - S - S (Side - Side - Side) congruence theorem, corresponding parts of congruent triangles are congruent (CPCTC).

Step2: Identify corresponding angles

$\angle ZWY$ and $\angle XWY$ are corresponding angles as $WY$ is a common side, $WZ = WX$ and $YZ=YX$ (from S - S - S congruence). Diagonal $WY$ bisects $\angle ZWX$. Also, $\angle ZYW$ and $\angle XYW$ are corresponding angles.
We can conclude that $\angle ZWX$ and $\angle ZYX$ are equal because corresponding parts of congruent triangles are equal.

Answer:

We can conclude that $\angle ZWX$ and $\angle ZYX$ are equal because when $\triangle WYZ\cong\triangle WYX$ (by S - S - S congruence), corresponding angles of congruent triangles (CPCTC) are congruent. $\angle ZWX$ and $\angle ZYX$ are corresponding angles of the congruent triangles $\triangle WYZ$ and $\triangle WYX$.