Question

vw = wx and ux = uv. complete the proof that ∠xwu ≅ ∠vwu.

statement
1 (overline{vw} cong overline{wx})
2 (overline{ux} cong overline{uv})
3 (overline{uw} cong overline{uw})
4

reason
given
given
reflexive property of congruence

Explanation:

Step1: Recall the SSS (Side - Side - Side) Congruence Criterion

The SSS congruence criterion states that if three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.

Step2: Identify the triangles and their sides

We have two triangles: \(\triangle VWU\) and \(\triangle WXU\).
We know that \(\overline{VW}\cong\overline{WX}\) (given), \(\overline{UX}\cong\overline{UV}\) (given), and \(\overline{UW}\cong\overline{UW}\) (reflexive property of congruence).

Step3: Apply the SSS Criterion

By the SSS (Side - Side - Side) congruence criterion, \(\triangle VWU\cong\triangle WXU\) since \(VW = WX\), \(UX = UV\), and \(UW=UW\)

Answer:

\(\triangle VWU\cong\triangle WXU\) by the SSS (Side - Side - Side) congruence criterion.