Question

vw ≅ vx. complete the proof that △vwx ≅ △vxw.

1 vw ≅ vx given
2 ∠v ≅ ∠v reflexive property of congruence
3 △vwx ≅ △vxw

Explanation:

Step1: Identify the given information

We are given that \(\overline{VW}\cong\overline{VX}\) (Statement 1) and \(\angle V\cong\angle V\) (Statement 2 by Reflexive Property of Congruence).

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

In \(\triangle VWX\) and \(\triangle VXW\), we have:

• Side: \(\overline{VW}\cong\overline{VX}\) (given)
• Angle: \(\angle V\cong\angle V\) (common angle, Reflexive Property)
• Side: \(\overline{VX}\cong\overline{VW}\) (since \(\overline{VW}\cong\overline{VX}\) is given, and congruence is symmetric, but also we can note that in the two triangles \(\triangle VWX\) and \(\triangle VXW\), if we consider the order of sides and angles for SAS: for \(\triangle VWX\) and \(\triangle VXW\), the sides adjacent to the common angle \(\angle V\) are \(\overline{VW}\) and \(\overline{VX}\) which are congruent.

By the Side - Angle - Side (SAS) congruence criterion, 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.

Answer:

The reason for Statement 3 (\(\triangle VWX\cong\triangle VXW\)) is the Side - Angle - Side (SAS) Congruence Criterion.