Question Choose ALL answers that describe the polygon \( N O P Q \) if \( N O=41, O P=57, P Q=19 \) \( Q N=61 \), and \( \overline{N O} \| \overline{P Q} \). Answer Attempt 1 out of 2 Parallelogram Video Quadrilateral Rectangle Rhombus Square Trapezoid

1. We are given a quadrilateral \( NOPQ \) with sides \[ NO=41,\quad OP=57,\quad PQ=19,\quad QN=61, \] and with \(\overline{NO}\parallel\overline{PQ}\). 2. A quadrilateral is defined as a polygon with four sides. Since \( NOPQ \) has four sides, it is by definition a quadrilateral. 3. A trapezoid (in many texts defined as a quadrilateral with at least one pair of parallel sides) fits this description. Here, since \(\overline{NO}\parallel\overline{PQ}\), \( NOPQ \) is a trapezoid. 4. A parallelogram requires both pairs of opposite sides to be parallel. We only know that \(\overline{NO}\parallel\overline{PQ}\); there is no information that \(\overline{OP}\parallel\overline{QN}\). In addition, the lengths of \( NO \) and \( PQ \) are different (\(41\) vs. \(19\)), which would contradict a parallelogram’s requirement of equal opposite sides. Thus, \( NOPQ \) is not a parallelogram. 5. A rectangle is a parallelogram with right angles. Since \( NOPQ \) is not even a parallelogram, it cannot be a rectangle. 6. A rhombus is a parallelogram with all sides of equal length. Since the side lengths differ, \( NOPQ \) is not a rhombus. 7. A square is a rectangle (and also a rhombus) with all sides equal. Therefore, \( NOPQ \) is not a square. The correct answers are: - Quadrilateral - Trapezoid