Question

△vwy is equilateral, ∠vyz ≅ ∠xwy, and overline{wx} ≅ overline{vz}. complete the proof that △wxy ≅ △vzy.

1 △vwy is equilateral given
2 ∠vyz ≅ ∠xwy given
3 overline{wx} ≅ overline{vz} given
4 overline{vy} ≅ overline{wy} definition of equilateral triangle
5

Explanation:

Step1: 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.

Step2: Identify the sides and angle for \(\triangle WXY\) and \(\triangle VZY\)

We are given that \(\overline{WX}\cong\overline{VZ}\) (side), \(\angle YVZ\cong\angle XWY\) (angle), and since \(\triangle VWY\) is equilateral, \(\overline{WY}\cong\overline{VY}\) (side).

Step3: Apply the SAS congruence criterion

For \(\triangle WXY\) and \(\triangle VZY\), we have \(\overline{WX}\cong\overline{VZ}\), \(\angle XWY\cong\angle YVZ\), and \(\overline{WY}\cong\overline{VY}\). So, by the SAS (Side - Angle - Side) congruence criterion, \(\triangle WXY\cong\triangle VZY\)

Answer:

\(\triangle WXY\cong\triangle VZY\) by the SAS (Side - Angle - Side) congruence criterion.