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Quadrilateral W X Y Z is shown. Diagonals are drawn from point W to point Y and from point Z to point X and intersect at point C. The lengths of W C and C Y are congruent.
Which best explains if quadrilateral WXYZ can be a parallelogram?
WXYZ is a parallelogram because diagonal XZ is bisected.
WXYZ is not necessarily a parallelogram because it is unknown if CZ = CY.
WXYZ is a parallelogram because ZC + CX = ZX.
WXYZ is not necessarily a parallelogram because it is unknown if WC = CY.
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Answer: "WXYZ is not necessarily a parallelogram because it is unknown if CZ = CX." (option 2)
Reason: A quadrilateral is a parallelogram iff its diagonals bisect each other, so you must have WC = CY and ZC = CX. You're only given WC = CY, so you don't know whether the other diagonal is bisected. Therefore you cannot conclude WXYZ is a parallelogram.
Reason: A quadrilateral is a parallelogram iff its diagonals bisect each other, so you must have WC = CY and ZC = CX. You're only given WC = CY, so you don't know whether the other diagonal is bisected. Therefore you cannot conclude WXYZ is a parallelogram.
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