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 \( \overline{VW}\cong\overline{VX}\), \( \overline{WY}\cong\overline{XY}\), and \( \overline{VY}\cong\overline{VY}\), by the SSS (Side - Side - Side) 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, \( \angle XVY\cong\angle WVY\) (Corresponding Parts of Congruent Triangles are Congruent - CPCTC).

Answer:

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