Question

wx || yz. complete the proof that △wyz ≅ △ywx.
statement
1 wx || yz
2 wx ≅ yz
3 ∠wyz ≅ ∠xyw
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 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.

Step2: Identify the sides and angle for the triangles \(\triangle WYZ\) and \(\triangle YWX\)

In \(\triangle WYZ\) and \(\triangle YWX\):

• We know that \(WZ\cong YX\) (given).
• \(\angle WYZ\cong\angle XYW\) (alternate interior angles as \(WX\parallel YZ\)).
• \(WY = WY\) (reflexive property of congruence).

Answer:

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