Question

tw bisects ∠utv and tv ≅ tu. complete the proof that uw ≅ vw.

Explanation:

Step1: Prove triangles congruent

Since \( \overline{TV}\cong\overline{TU}\), \( \angle UTW\cong\angle VTW\), and \( \overline{TW}\cong\overline{TW}\), by the Side - Angle - Side (SAS) congruence criterion, \( \triangle UTW\cong\triangle VTW\).

Step2: Use congruent triangles property

If two triangles are congruent, then their corresponding sides are congruent. So, \( \overline{UW}\cong\overline{VW}\) as they are corresponding sides of congruent triangles \( \triangle UTW\) and \( \triangle VTW\).

Answer:

1. \( \triangle UTW\cong\triangle VTW\); SAS Congruence Criterion
2. \( \overline{UW}\cong\overline{VW}\); Corresponding parts of congruent triangles are congruent (CPCTC)