Question

In the quadrilateral below. “Angle WXZ is congruent to Angle YZX." If Ricardo's conjecture is true, which of the following must be true for Quadrilateral WXYZ to be a parallelogram?

Answer 1

∠YXZ ≅ ∠WZX

Explanation:

Given that “Angle WXZ is congruent to Angle YZX."

The angles are shown in the diagram below.

This means that angles WXZ and YZX are alternate angles and thus,

• WX is parallel to ZY.

Consider the diagram below:

Angles YXZ and WZX are congruent by alternate angles, and thus:

• WZ is parallel to XY.

So, we have shown that the opposite sides of the quadrilateral are parallel.

Therefore, in order for quadrilateral WXYZ to be a parallelogram, Angles YXZ and WZX must be congruent.

The first option (∠YXZ ≅ ∠WZX ) is correct.