Question

Xander says that it is not possible to draw a quadrilateral that is not a parallelogram and not a trapezoid. Devin says it is possible. Explain who is correct.


A
Xander is correct because every trapezoid is a quadrilateral and a parallelogram.

B
Devin is correct because he can draw a quadrilateral with no pairs of parallel sides.

C
Xander is correct because both parallelograms and trapezoids have right angles.

D
Devin is right because parallelograms and trapezoids do not have the same number of sides.

Answer 1

A good place to start for this question is to define the properties of the geometric terms you are given.

Quadrilaterals have four straight sides. 

Parallelograms are quadrilaterals that have two pairs of parallel sides. The opposite sides and opposite angles are congruent. Squares, rectangles, and rhombuses are examples of parallelograms.

Trapezoids are also quadrilaterals. They have only one pair of parallel sides.

So we're looking to see if there are any four-sided shapes that can be made with no parallel sides. The attached picture shows an example of a quadrilateral that is not a parallelogram and is not a trapezoid. Based on these properties of polygons, the correct answer is B.