Question

Given: ∠XWU ≅ ∠ZVT; ∠ZTV ≅ ∠XUW; TU ≅ VW

Triangles Z V T and X W U overlap and intersect at point Y. Angles Z T U and W U W are congruent. Angles Z V T and X W U are congruent. Lines segment T U and V W are congruent. A line is drawn through point Y to point S on side X W and to point R on side Z T. Another line connects points Z and X.

Which relationship in the diagram is true?

△XYZ ≅ △XYS by SSS
△ZYX ≅ △VYU by AAS
△RYZ ≅ △XZY by SAS
△ZVT ≅ △XWU by ASA

Answer 1

△ZVT ≅ △XWU by ASA.

Reason: ∠ZVT ≅ ∠XWU and ∠ZTV ≅ ∠XUW (given), and the side between those two angles corresponds and is congruent (TU ≅ VW given). Thus the two triangles are congruent by Angle–Side–Angle.