Question

1. given: \\( \overline { wx } \parallel \overline { yz } , \overline { wx } \cong \overline { yz } \\) prove: \\( \triangle wxz \cong \triangle yzx \\)

Explanation:

Step1: Alternate interior angles

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

Step2: Side - Angle - Side (SAS) criterion

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

Answer:

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