Question

1. given: (overline{wx}paralleloverline{yz},overline{wx}congoverline{yz}) prove: (\triangle wxzcong\triangle yzx)

Explanation:

Step1: Identify the included angle

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

Step2: List the sides and included angle

We are given \(WX = YZ\) (given), \(XZ=ZX\) (common side), and \(\angle WXZ=\angle YZX\) (from Step 1)

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

By the SAS congruence criterion, if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the two triangles are congruent. So, \(\triangle WXZ\cong\triangle YZX\)

Answer:

The proof is completed as above, using the SAS (Side - Angle - Side) congruence criterion to show \(\triangle WXZ\cong\triangle YZX\)