Question

uv || wx. complete the proof that \\( \triangle uvw \cong \triangle wxu \\).

Explanation:

Step1: Analyze the given information

We are given that \(\overline{WX}\cong\overline{UV}\), \(\overline{UV}\parallel\overline{WX}\), \(\angle UWX\cong\angle VUW\) (by Alternate - Interior Angles Theorem as \(\overline{UV}\parallel\overline{WX}\) and \(\overline{UW}\) is a transversal), and \(\overline{UW}\cong\overline{UW}\) (Reflexive Property of Congruence).

Step2: 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.
In \(\triangle UVW\) and \(\triangle WXU\), we have:

• Side: \(\overline{WX}\cong\overline{UV}\) (Given)
• Angle: \(\angle UWX\cong\angle VUW\) (Alternate Interior Angles Theorem)
• Side: \(\overline{UW}\cong\overline{UW}\) (Reflexive Property of Congruence)

Answer:

SAS