Question

∠sxt≅∠uvw, overline{wx}≅overline{tu}, and ∠tsx≅∠uvw. complete the proof that overline{sx}≅overline{vw}.

Explanation:

Step1: Recall the ASA (Angle - Side - Angle) Congruence Criterion

The ASA congruence criterion states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.
In \(\triangle STX\) and \(\triangle VUW\), we have \(\angle SXT\cong\angle UWV\) (given), \(TX = UW\) (from step 7: \(UW = TX\)), and \(\angle TSX\cong\angle UVW\) (given).

Step2: Apply the ASA Criterion

Since \(\angle SXT\cong\angle UWV\), \(TX = UW\), and \(\angle TSX\cong\angle UVW\), by the ASA (Angle - Side - Angle) congruence criterion, \(\triangle STX\cong\triangle VUW\).

Answer:

ASA (Angle - Side - Angle)