Question

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

Explanation:

Step1: Identify the common side

$$\overline{XZ}\cong\overline{XZ}$$ (Reflexive property of congruence).

Step2: Use the property of parallel lines

Since \(WX\parallel YZ\), then \(\angle WXZ\cong\angle YZX\) (Alternate - interior angles theorem).

Step3: Apply the SAS (Side - Angle - Side) congruence criterion

We know that \(WX = YZ\) (given), \(\angle WXZ\cong\angle YZX\) (from step 2), and \(\overline{XZ}\cong\overline{XZ}\) (from step 1). By the SAS congruence criterion, \(\triangle WXZ\cong\triangle YZX\).

Answer:

\(\triangle WXZ\cong\triangle YZX\) (by SAS congruence criterion: \(WX = YZ\) (given), \(\angle WXZ\cong\angle YZX\) (alternate - interior angles as \(WX\parallel YZ\)), \(\overline{XZ}\cong\overline{XZ}\) (reflexive property)).