Question

(overline{vx}congoverline{vy},angle yvzcongangle wvx,) and (angle vywcongangle vxz). complete the proof that (overline{wy}congoverline{xz}).

Explanation:

Step1: Recall the ASA (Angle - Side - Angle) Congruence Criterion

If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

Step2: Identify the triangles

We want to show that \(\triangle WVY\cong\triangle XVZ\).
We know that \(\overline{VX}\cong\overline{VY}\) (given).
We have \(m\angle WVY=m\angle XVZ\) (from step 7).
Also, \(\angle VYW\cong\angle VXZ\) (given).

Step3: Apply ASA Congruence

In \(\triangle WVY\) and \(\triangle XVZ\):

• \(\overline{VX}\cong\overline{VY}\) (side)
• \(\angle WVY\cong\angle XVZ\) (angle)
• \(\angle VYW\cong\angle VXZ\) (angle)

By ASA congruence criterion, \(\triangle WVY\cong\triangle XVZ\).

Step4: Use CPCTC (Corresponding Parts of Congruent Triangles are Congruent)

Since \(\triangle WVY\cong\triangle XVZ\), then \(\overline{WY}\cong\overline{XZ}\)

Answer:

\(\triangle WVY\cong\triangle XVZ\) (by ASA) and \(\overline{WY}\cong\overline{XZ}\) (by CPCTC)