Question

To prove quadrilateral WXYZ is a parallelogram, Travis begins by proving △WZY ≅ △YXW by using the SAS congruency theorem. Which reasons can Travis use to prove the two triangles are congruent? Check all that apply.

Answer 1

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

[B] WY ≅ WY by the reflexive property.

[E] WZ ≅ XY by the given.

Step-by-step explanation:

Answer 2

∠ZWY ≅ ∠XYW by the alternate interior ∠s theorem,

WY ≅ WY by the reflexive property

WZ ≅ XY by the given.

Step-by-step explanation:

The option:

• WX ≅ ZY by definition of a parallelogram

can't be used because we want to prove that WXYZ is a parallelogram

The Alternate Interior Angles Theorem states that, when two parallel lines (here XY and WZ) are cut by a transversal (here WY), the resulting alternate interior angles (here ∠ZWY and ∠XYW ) are congruent.

The reflexive property of congruence states that an angle, line segment, or shape is always congruent to itself. Here, WY ≅ WY.