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Answer :
Final answer:
In a special trapezoid like quadrilateral wxyz, only one pair of opposite sides are parallel, making option b) WX is parallel to ZY a possible truth about the quadrilateral.
Explanation:
Quadrilateral wxyz is a special trapezoid. In a trapezoid, only one pair of opposite sides are parallel. Therefore, in quadrilateral wxyz, one of the statements must be true. To determine which is true, we need to remember the properties of trapezoids and parallel lines.
- a) WX is parallel to WZ: This statement would make WX and WZ parallel, which is not possible in a trapezoid where only one pair of opposite sides is parallel.
- b) WX is parallel to ZY: This statement could be true in a trapezoid, as WX and ZY could be parallel in this case.
- c) XW is parallel to XY: This statement is not likely as XW and XY would be intersecting, not parallel.
- d) WY is parallel to XZ: This statement would also result in two pairs of parallel sides, which is inconsistent with the properties of a trapezoid.
Therefore, based on the properties of trapezoids, option b) WX is parallel to ZY could be true about quadrilateral wxyz.
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