1. **Problem Statement:** Determine which statement can be used to conclude that quadrilateral XYZW is a parallelogram. 2. **Key Concept:** A quadrilateral is a parallelogram if both pairs of opposite sides are congruent. 3. **Given Statements:** - XW \cong YZ and XY \cong WZ - XW \cong YZ and XY \cong WZ (repeated) - XW \cong YZ and XY \cong YZ - YN \cong NX and XN \cong NY 4. **Analysis:** - The first statement says opposite sides XW and YZ are congruent, and opposite sides XY and WZ are congruent. This matches the parallelogram condition. - The third statement says XY \cong YZ, which are adjacent sides, not opposite. - The fourth statement involves segments related to diagonals intersecting at N, which does not directly prove parallelogram. 5. **Conclusion:** The correct statement to conclude XYZW is a parallelogram is: $$\text{XW} \cong \text{YZ} \quad \text{and} \quad \text{XY} \cong \text{WZ}$$ This satisfies the condition that both pairs of opposite sides are congruent, which is a defining property of parallelograms.