Question

beginning a proof of the single opposite side theorem
to prove quadrilateral wxyy 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? choose three correct answers.
(overline{wz}congoverline{xy}) by the given.
(overline{wy}congoverline{wy}) by the reflexive property.

Explanation:

• For \(\overline{WZ}\cong\overline{XY}\): In a parallelogram proof, if we assume the property of opposite sides (which is often given or can be derived from the figure's markings). Here, \(\overline{WZ}\) and \(\overline{XY}\) are likely marked as equal (given) in the context of proving the quadrilateral is a parallelogram.
• For \(\overline{WY}\cong\overline{WY}\): The reflexive property of congruence states that any segment is congruent to itself. So, the common side \(WY\) in \(\triangle WZY\) and \(\triangle YXW\) satisfies \(\overline{WY}\cong\overline{WY}\) by the reflexive property.
• For \(\angle WZY\cong\angle YXW\) (assuming this is the third reason, as we need three reasons for SAS): If \(WZ\parallel XY\) (a property of a parallelogram which we are trying to prove, but in the context of using SAS, alternate - interior angles are congruent. When \(WZ\parallel XY\) and \(WY\) is a transversal, \(\angle WZY\) and \(\angle YXW\) are alternate - interior angles, so \(\angle WZY\cong\angle YXW\) by the alternate - interior angles theorem.

Answer:

\(\overline{WZ}\cong\overline{XY}\) by the given; \(\overline{WY}\cong\overline{WY}\) by the reflexive property; \(\angle WZY\cong\angle YXW\) by the alternate - interior angles theorem.