Question

Consider the following special trapezoid with angles ∠W and ∠Z. Given this configuration, which of the following statements can be proven true?

A. WX is parallel to WZ.
B. WX is parallel to ZY.
C. WY is parallel to XZ.
D. XW is parallel to XY.

Answer 1

In the given trapezoid, ∠W and ∠Z are linear pairs. WX and ZY are alternate interior angles and must be congruent. Therefore, the statement that can be proven true is B. WX is parallel to ZY.

Step-by-step explanation:

In the given trapezoid, ∠W and ∠Z are adjacent angles. Adjacent angles are supplementary, which means they add up to 180 degrees. Since ∠W and ∠Z are adjacent and their sum is 180 degrees, ∠W and ∠Z are linear pairs.

When two parallel lines are intersected by a transversal, alternate interior angles are congruent. In this case, transversal WX intersects parallel lines WZ and YZ. So, WX and ZY are alternate interior angles, and they must be congruent.

Therefore, the statement that can be proven true is B. WX is parallel to ZY.