Question

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

Explanation:

Step1: Recall congruent - triangle property

If \(\triangle WYZ\cong\triangle WYX\) by SSS (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, and \(\angle ZYW\) and \(\angle XYW\) are corresponding angles.
Since corresponding parts of congruent triangles are congruent, \(\angle ZWY=\angle XWY\) and \(\angle ZYW = \angle XYW\). This means that \(WY\) bisects \(\angle ZWX\) and \(\angle ZYX\).

Answer:

He can conclude that diagonal \(WY\) bisects angles \(ZWX\) and \(ZYX\) because corresponding parts of congruent triangles are congruent. When \(\triangle WYZ\cong\triangle WYX\) by SSS, the angles formed by the diagonal \(WY\) with the sides of the angles \(ZWX\) and \(ZYX\) are equal, which is the definition of an angle - bisector.