Question

wx || yz. complete the proof that △wyz ≅ △ywx.
statement
1 wx || yz
2 wx ≅ yz
3 ∠wyz ≅ ∠xwy
4 wy ≅ wy
5
reason
given
given
alternate interior angles theorem
reflexive property of congruence

Explanation:

Step1: Analyze the given information

We know that \(\overline{WX}\parallel\overline{YZ}\), \(\overline{WX}\cong\overline{YZ}\), \(\angle WYZ\cong\angle XWY\) (from alternate - interior angles as \(\overline{WX}\parallel\overline{YZ}\) and transversal \(\overline{WY}\)), and \(\overline{WY}\cong\overline{WY}\) (reflexive property).

Step2: Use the SAS (Side - Angle - Side) congruence criterion

The SAS congruence criterion states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.
In \(\triangle WYZ\) and \(\triangle YWX\), we have \(\overline{WX}\cong\overline{YZ}\), \(\angle WYZ\cong\angle XWY\), and \(\overline{WY}\cong\overline{WY}\).

Answer:

\(\triangle WYZ\cong\triangle YWX\) (by SAS congruence criterion)