Question

given: wx || yz, wz ≅ wx, yz ≅ yz
prove: △wxz ≅ △yzx

Explanation:

Step1: Use the property of parallel lines

Since \( WX\parallel YZ\), then \(\angle WXZ=\angle YZX\) (alternate - interior angles).

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

We know that \( WX = YZ\) (given), \(\angle WXZ=\angle YZX\) (from Step 1), and \( XZ = ZX\) (common side).
By the SAS congruence criterion, \(\triangle WXZ\cong\triangle YZX\).

Answer:

\(\triangle WXZ\cong\triangle YZX\) is proved by the Side - Angle - Side (SAS) congruence criterion.