Question

w is the midpoint of \\( \overline{vx} \\). complete the proof that \\( \triangle vwy \cong \triangle wxz \\).

Explanation:

Step1: Recall the 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.

Step2: Identify the sides of the triangles

In \(\triangle VWY\) and \(\triangle WXZ\), we have \(\overline{VW}\cong\overline{WX}\) (from the definition of mid - point, statement 4), \(\overline{WY}\cong\overline{XZ}\) (statement 3), and \(\overline{VY}\cong\overline{WZ}\) (statement 2).

Answer:

\(\triangle VWY\cong\triangle WXZ\) by the SSS (Side - Side - Side) congruence criterion.