Question

to prove quadrilateral wxyz is a parallelogram, travis begins by proving △wzy≅△yxw by using the sas congruency theorem. which reasons can travis use to prove the two triangles are congruent? check all that apply. ∠zwy≅∠xyw by the alternate interior ∠s theorem. wy≅wy by the reflexive property. ∠zwy≅∠xwy by the corresponding ∠s theorem. wx≅zy by definition of a parallelogram wz≅xy by the given.

Explanation:

1. For the Side - Angle - Side (SAS) congruency theorem, we need two sides and the included angle to be congruent.

• $\angle ZWY\cong\angle XYW$ by the alternate - interior angles theorem. If $WX\parallel ZY$ (which is a property of a parallelogram), then these alternate - interior angles formed by the transversal $WY$ are congruent. This gives us the included angle for SAS.
• $\overline{WY}\cong\overline{WY}$ by the reflexive property. This is the common side for the two triangles $\triangle WZY$ and $\triangle YXW$.
• $\overline{WZ}\cong\overline{XY}$ by the given (if it is given in the problem - context). This gives us one of the non - common sides for SAS.
• $\angle ZWY$ and $\angle XWY$ are not corresponding angles in the context of proving $\triangle WZY\cong\triangle YXW$.
• $\overline{WX}\cong\overline{ZY}$ is a property of a parallelogram, but it is not directly used in the SAS proof of these two triangles.

Answer:

• $\angle ZWY\cong\angle XYW$ by the alternate interior $\angle s$ theorem.
• $\overline{WY}\cong\overline{WY}$ by the reflexive property.
• $\overline{WZ}\cong\overline{XY}$ by the given.