Question

vy bisects ∠wvx. complete the proof that △vxy ≅ △vwy.
1 vy bisects ∠wvx given
2 vw ≅ vx given
3 ∠wvy ≅ ∠xvy definition of angle bisector
4 vy ≅ vy reflexive property of congruence
5 △vxy ≅ △vwy cpctc definition of congruence sas sss

Explanation:

Step1: Identify the given information

We are given that \(\overrightarrow{VY}\) bisects \(\angle WVX\) (so \(\angle WVY=\angle XVY\)), \(\overline{VW}\cong\overline{VX}\), and \(\overline{VY}\cong\overline{VY}\) (reflexive property).

Step2: Recall the SAS (Side - Angle - Side) congruence criterion

The SAS congruence criterion states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.
In \(\triangle VXY\) and \(\triangle VWY\), we have \(\overline{VW}\cong\overline{VX}\) (side), \(\angle WVY\cong\angle XVY\) (angle), and \(\overline{VY}\cong\overline{VY}\) (side).

Answer:

SAS