Question

choose all answers that describe the polygon defg if de = 13, ef = 18, fg = 13, gd = 18, \overline{de} \parallel \overline{fg}, and \overline{ef} \parallel \overline{gd}.

Explanation:

Step1: Check the definition of quadrilateral

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

Step2: Check the definition of parallelogram

A parallelogram is a quadrilateral with two pairs of parallel sides. Given \(\overline{DE}\parallel\overline{FG}\) and \(\overline{EF}\parallel\overline{GD}\), \(DEFG\) satisfies the definition of a parallelogram.

Step3: Analyze for rectangle, rhombus, square

For a rectangle, all angles should be right - angles (not given). For a rhombus, all sides should be equal (\(DE = 13\), \(EF=18\), sides are not all equal). For a square, it should be both a rectangle and a rhombus (fails as above).

Step4: Analyze for trapezoid

A trapezoid has only one pair of parallel sides. But \(DEFG\) has two pairs of parallel sides, so it is not a trapezoid.

Answer:

• Parallelogram
• Quadrilateral