Question

choose all answers that describe the polygon nopq if no = 10, op = 18, pq = 10, qn = 18, \overline{no} \parallel \overline{pq}, and \overline{op} \parallel \overline{qn}.
answer attempt 1 out of 2
parallelogram
quadrilateral
rectangle
rhombus
square
trapezoid

Explanation:

1. Quadrilateral: A polygon with four sides. \(NOPQ\) has four sides (\(NO\), \(OP\), \(PQ\), \(QN\)), so it is a quadrilateral.
2. Parallelogram: A quadrilateral with both pairs of opposite sides parallel and equal. Here, \(\overline{NO} \parallel \overline{PQ}\) and \(NO = PQ = 10\); \(\overline{OP} \parallel \overline{QN}\) and \(OP = QN = 18\), so it satisfies the parallelogram definition.
3. Rectangle: A parallelogram with four right angles. We don't know if angles are right angles (sides are \(10\) and \(18\), not equal, so not a rhombus/square, and no info on right angles), so not a rectangle.
4. Rhombus: A parallelogram with all sides equal. Sides are \(10\) and \(18\) (not all equal), so not a rhombus.
5. Square: A rhombus and rectangle (all sides equal, all angles right). Fails both, so not a square.
6. Trapezoid: A quadrilateral with at least one pair of parallel sides. But a parallelogram has two pairs, and trapezoid (in some definitions) has exactly one, but here it's a parallelogram, so not a trapezoid (in exclusive definition) or if inclusive, but parallelogram is a better fit.

Answer:

A. Parallelogram, B. Quadrilateral