Question

complete the proof that ( \triangle twx cong \triangle uvx ).

Explanation:

Step1: 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.

Step2: Identify the triangles and their corresponding parts

We have \(\triangle TWX\) and \(\triangle UVX\). We know that \(\overline{WX}\cong\overline{VX}\) (given), \(\overline{UX}\cong\overline{TX}\) (given), and \(\angle TXW\cong\angle UXV\) (vertical angle theorem).

Answer:

\(\triangle TWX\cong\triangle UVX\) by the SAS (Side - Angle - Side) congruence criterion.