Question

question
choose all answers that describe the quadrilateral uvwx if \\(\overline{uv} \parallel \overline{wx}\\), \\(uv = 9\\), and \\(wx = 9\\).
answer
parallelagram
rectangle
rhombus
square
trapezoid

Explanation:

Step1: Recall the definitions

A parallelogram has both pairs of opposite sides parallel and equal. A rectangle is a parallelogram with four right - angles. A rhombus is a parallelogram with all sides equal. A square is a parallelogram with all sides equal and four right - angles. A trapezoid has only one pair of parallel sides.
Since \(UV\parallel WX\) and \(UV = WX=9\), by the definition of a parallelogram (a quadrilateral with one pair of opposite sides parallel and equal is a parallelogram), \(UVWX\) is a parallelogram.
A rectangle is a parallelogram. A rhombus is a parallelogram. A square is a parallelogram. But we have no information about angles or the lengths of the other pair of sides. So we cannot confirm it is a rectangle, rhombus or square.
A trapezoid has only one pair of parallel sides. Here, if we assume it is a parallelogram (two pairs of parallel sides), it cannot be a trapezoid.

Answer:

Parallelogram