Question

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?
since ▼ parts of congruent triangles are ▼, angle zwy is congruent to angle ▼ and angle zyw is congruent to angle ▼. therefore, wy must be the angle bisector.
graphing calculator

Explanation:

When two triangles are congruent (by SSS here), their corresponding parts (angles and sides) are congruent. For congruent triangles \( \triangle WYZ\) and \( \triangle WYX\), the corresponding angles \( \angle ZWY\) and \( \angle XWY\) (which are formed by the diagonal \( WY\) with sides \( WZ\) and \( WX\) respectively) are congruent. Also, \( \angle ZYW\) and \( \angle XYW\) (formed by the diagonal \( WY\) with sides \( YZ\) and \( YX\) respectively) are congruent. Since a ray that divides an angle into two congruent angles is an angle - bisector, \( WY\) bisects \( \angle ZWX\) (because \( \angle ZWY=\angle XWY\)) and \( \angle ZYX\) (because \( \angle ZYW = \angle XYW\)).

Answer:

1. corresponding
2. congruent
3. \( \angle XWY\)
4. \( \angle XYW\)