Question

△vyz≅△xwz. complete the proof that △xyz≅△vwz.

1 △vyz≅△xwz given
2 \\( \overline { vz } \cong \overline { xz } \\) cpctc
3 \\( \overline { wz } \cong \overline { yz } \\) cpctc
4 \\( \angle vzw \cong \angle xzy \\) vertical angle theorem
5 △xyz≅△vwz

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 included angle for \(\triangle XYZ\) and \(\triangle VWZ\)

From statement 2 (\(\overline{VZ}\cong\overline{XZ}\)), statement 3 (\(\overline{WZ}\cong\overline{YZ}\)), and statement 4 (\(\angle VZW\cong\angle XZY\)). In \(\triangle XYZ\) and \(\triangle VWZ\), we have two sides (\(\overline{XZ}\cong\overline{VZ}\), \(\overline{YZ}\cong\overline{WZ}\)) and the included angle (\(\angle XZY\cong\angle VZW\))

Answer:

\(\text{SAS (Side - Angle - Side) Congruence Criterion}\)