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To prove quadrilateral WXYZ is a parallelogram, Travis begins by proving △WZY ≅ △YXW by using the SAS congruency theorem.

Quadrilateral W X Y Z is shown. A diagonal is drawn from point W to point Y. Sides W Z and X Y are parallel and congruent.

Which reasons can Travis use to prove the two triangles are congruent? Check all that apply.
∠ZWY ≅ ∠XYW by the alternate interior ∠s theorem.
WY ≅ WY by the reflexive property.
∠ZWY ≅ ∠XWY by the corresponding ∠s theorem.
WX ≅ ZY by definition of a parallelogram.
WZ ≅ XY by the given.

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akposevictor

The reasons Travis can use to prove both triangles are congruent by the SAS congruency theorem are:

  • ∠ZWY ≅ ∠XYW by the alternate interior ∠s theorem.
  • WY ≅ WY by the reflexive property.
  • WZ ≅ XY by the given.

What is the SAS Congruency Theorem?

The SAS congruency theorem states that two triangles are congruent when they both have two pairs of corresponding congruent sides and a pair of corresponding congruent included angles.

Given the image below, we have the following proof with the statement and reasons in bracket:

WZ ≅ XY [given]

WY ≅ WY [reflexive property]

∠ZWY ≅ ∠XYW [by the alternate interior ∠s theorem]

△WZY ≅ △YXW [by the SAS congruency theorem]

Therefore, the reasons Travis can use are:

  • ∠ZWY ≅ ∠XYW by the alternate interior ∠s theorem.
  • WY ≅ WY by the reflexive property.
  • WZ ≅ XY by the given.

Learn more about the SAS congruency theorem on:

https://brainly.com/question/2102943

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