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: Recall the SAS (Side - Angle - Side) Congruence Criterion

The SAS 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.

Step2: Identify the corresponding parts

We have \( \overline{WX}\cong\overline{YZ}\) (given), \( \angle WYZ\cong\angle XWY\) (alternate interior angles as \( \overline{WX}\parallel\overline{YZ}\)), and \( \overline{WY}\cong\overline{WY}\) (reflexive property).

Step3: Apply the SAS Criterion

For \( \triangle WYZ\) and \( \triangle YWX\), in \( \triangle WYZ\) and \( \triangle YWX\), we have:

• Side: \( \overline{WX}\cong\overline{YZ}\)
• Angle: \( \angle WYZ\cong\angle XWY\)
• Side: \( \overline{WY}\cong\overline{WY}\)

So, by the SAS (Side - Angle - Side) congruence criterion, \( \triangle WYZ\cong\triangle YWX\)

Answer:

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