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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

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Answer:

d

Step-by-step explanation:

akposevictor

The relationship between △ZVT and △XWU based on a congruence theorem is: D. △ZVT ≅ △XWU by ASA

Recall:

  • The Angle-Side-Angle Congruence Theorem states that if a triangle has two angles and an included side that are congruent to two corresponding sides and an included angle of another triangle, both triangles are considered congruent to each other.

Fromm the information given to us about △ZVT and △XWU, we have the following:

  • Two pairs of congruent angles
  • A pair of congruent included side

Therefore, the relationship between △ZVT and △XWU based on a congruence theorem is: D. △ZVT ≅ △XWU by ASA

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