9
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Proving a Quadrilateral Is a Parallelogram

Question 9 • *CR CCSS Math 2 S2 [M2960OX]

Which reasons can Travis use to prove the two triangles are congruent? Check all that apply.

Answer
A
∠ZWY ≅ ∠XYW by the alternate interior ∠s theorem.
B
WY ≅ WY by the reflexive property.
C
∠ZWY ≅ ∠XWY by the corresponding ∠s theorem.
D
WX ≅ ZY by definition of a parallelogram.
E
WZ ≅ XY by the given.

Explanation

The triangles are congruent by SAS. The angles ∠ZWY and ∠XYW are congruent by the alternate interior angles theorem (A), and WY is shared by both triangles, so WY ≅ WY by the reflexive property (B). The given WZ ≅ XY supplies the other pair of corresponding sides (E).

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