Question

y is the midpoint of \\( \overline{wx} \\). complete the proof that \\( \angle xvy \cong \angle wvy \\).

Explanation:

Step1: Determine the congruence of triangles

Since \( \overline{VW}\cong\overline{VX}\) (given), \( \overline{WY}\cong\overline{XY}\) (definition of mid - point), and \( \overline{VY}\cong\overline{VY}\) (reflexive property of congruence), by the Side - Side - Side (SSS) congruence criterion, \( \triangle VWY\cong\triangle VXY\).

Step2: Use the property of congruent triangles

If two triangles are congruent, then their corresponding parts are congruent. So, if \( \triangle VWY\cong\triangle VXY\), then \( \angle XVY\cong\angle W VY\) (corresponding parts of congruent triangles are congruent).

Answer:

1. SSS Congruence Criterion; 6. Corresponding Parts of Congruent Triangles are Congruent (CPCTC)