Question

choose all answers that describe the polygon defg if de = 13, ef = 18, fg = 13, gd = 18, \\( \overline { d e } \parallel \overline { f g } \\), and \\( \overline { e f } \parallel \overline { g d } \\)
answer
parallelogram
quadrilateral
rectangle
rhombus
square
trapezoid

Explanation:

Step1: Analyze the number of sides

A polygon with four sides is a quadrilateral. Since DEFG has four sides (DE, EF, FG, GD), it is a quadrilateral.

Step2: Check the properties of a parallelogram

A parallelogram has two pairs of parallel sides. Here, \(\overline{DE}\parallel\overline{FG}\) and \(\overline{EF}\parallel\overline{GD}\), so it is a parallelogram.

Step3: Check for rectangle, rhombus, square

A rectangle requires all angles to be \(90^{\circ}\) (not given). A rhombus requires all sides equal (\(DE = 13\), \(EF=18\), sides are not all equal). A square requires all sides equal and all angles \(90^{\circ}\) (not met). A trapezoid has only one pair of parallel sides (here two pairs, so not a trapezoid).

Answer:

Parallelogram, Quadrilateral