Question

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

Explanation:

Step1: Vertical angles are congruent

$\angle XWZ\cong\angle VWY$ (Vertical angles are congruent)

Step2: Use SSS congruence criterion

In $\triangle WXZ$ and $\triangle W V Y$, we have

• $\overline{WX}\cong\overline{WV}$ (Since \(W\) is the mid - point of \(\overline{VX}\), by the definition of mid - point)
• $\overline{WY}\cong\overline{WZ}$ (Given)
• $\overline{XZ}\cong\overline{VY}$ (Given)
• $\angle XWZ\cong\angle VWY$ (Vertical angles)

By the Side - Side - Side (SSS) congruence criterion, $\triangle WXZ\cong\triangle W V Y$

Answer:

1. $\angle XWZ\cong\angle VWY$; Vertical angles are congruent
2. $\triangle WXZ\cong\triangle W V Y$; SSS (Side - Side - Side) congruence criterion