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:

Step1: Recall SAS congruency

SAS (Side - Angle - Side) requires two pairs of congruent sides and the included angles to be congruent.

Step2: Analyze angle congruence

$\angle ZWY\cong\angle XYW$ by the alternate - interior angles theorem. When two parallel lines are cut by a transversal, alternate - interior angles are congruent. In a parallelogram, opposite sides are parallel, and here $\overline{WZ}\parallel\overline{XY}$, so this angle congruence can be used.

Step3: Analyze side congruence

$\overline{WY}\cong\overline{WY}$ by the reflexive property. This is the common side for both $\triangle WZY$ and $\triangle YXW$.

Step4: Analyze other side congruence

$\overline{WZ}\cong\overline{XY}$ is given (from the markings on the figure).

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.