Question

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.

Explanation:

Step1: Recall parallelogram property

One of the properties of a parallelogram is that its diagonals bisect each other. In a quadrilateral \(WXYZ\) with diagonals \(XZ\) and \(WY\) intersecting at \(C\), for it to be a parallelogram, we need \(WC = CY\) and \(ZC=CX\).

Step2: Analyze given options

The first option only says diagonal \(XZ\) is bisected, but we need both diagonals to bisect each other. The second - option about \(CZ = CY\) is not the key condition for diagonals bisecting each other. The third option \(ZC + CX=ZX\) is just the segment - addition postulate and not a condition for a parallelogram. The fourth option is correct because for \(WXYZ\) to be a parallelogram, we need to know if \(WC = CY\) (in addition to \(ZC = CX\)) and since it is unknown if \(WC = CY\), \(WXYZ\) is not necessarily a parallelogram.

Answer:

WXYZ is not necessarily a parallelogram because it is unknown if WC = CY.