Question

1. based only on the information given, can you determine that the quadrilateral must be a parallelogram? explain. given: $overline{xn}congoverline{nz}$ and $overline{ny}congoverline{nw}$

Explanation:

Step1: Recall parallelogram property

One property of a parallelogram is that its diagonals bisect each other.

Step2: Analyze given information

Given $\overline{XN}\cong\overline{NZ}$ and $\overline{NY}\cong\overline{NW}$, it means the diagonals $\overline{XZ}$ and $\overline{YW}$ bisect each other at point $N$.

Step3: Apply the theorem

If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.

Answer:

Yes, the quadrilateral must be a parallelogram because the diagonals $\overline{XZ}$ and $\overline{YW}$ bisect each other (since $\overline{XN}\cong\overline{NZ}$ and $\overline{NY}\cong\overline{NW}$), and a quadrilateral with bisecting diagonals is a parallelogram.