Question

y is the midpoint of \\( \overline { w x } \\). complete the proof that \\( \triangle v x y \cong \triangle v w y \\).

Explanation:

Step1: Reflexive property of congruence

For any segment \( \overline{AB} \), \( \overline{AB}\cong\overline{AB} \). In this case, for segment \( \overline{VY} \), we have \( \overline{VY}\cong\overline{VY} \) by the reflexive property of congruence.

Step2: SSS (Side - Side - Side) congruence criterion

The SSS congruence criterion states that if three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.
We know that \( \overline{VX}\cong\overline{VW} \) (given), \( \overline{WY}\cong\overline{XY} \) (definition of mid - point), and \( \overline{VY}\cong\overline{VY} \) (reflexive property).
So, \( \triangle VXY\cong\triangle VWY\) by the SSS (Side - Side - Side) congruence criterion.

Answer:

1. Reflexive property of congruence; 5. SSS (Side - Side - Side) congruence criterion.