Question

complete the proof that ( \triangle vyz cong \triangle wxz ).

Explanation:

Step1: Recall the Side - Angle - Side (SAS) Congruence Theorem

The SAS congruence theorem 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 corresponding parts in \(\triangle VYZ\) and \(\triangle WXZ\)

We have \(\overline{WZ}\cong\overline{VZ}\) (given), \(\overline{XZ}\cong\overline{YZ}\) (given), and \(\angle VZY\cong\angle WZX\) (vertical angle theorem). The angle \(\angle VZY\) is the included angle for sides \(\overline{VZ}\) and \(\overline{YZ}\) in \(\triangle VYZ\), and \(\angle WZX\) is the included angle for sides \(\overline{WZ}\) and \(\overline{XZ}\) in \(\triangle WXZ\)

Answer:

By the Side - Angle - Side (SAS) Congruence Theorem, \(\triangle VYZ\cong\triangle WXZ\)