Question

choose all answers that describe the polygon defg if ( mangle d=mangle e ), ( mangle f=mangle g ), and ( overline{de}paralleloverline{fg} ).
answer
parallelogram
quadrilateral
rectangle
rhombus
square
trapezoid

Explanation:

• Quadrilateral: A polygon with four sides. Since \(DEFG\) has four sides (\(DE\), \(EF\), \(FG\), \(GD\)), it is a quadrilateral.
• Trapezoid: A trapezoid is a quadrilateral with at least one pair of parallel sides. Here, \(\overline{DE}\parallel\overline{FG}\), so \(DEFG\) is a trapezoid.
• Parallelogram: A parallelogram has two pairs of parallel sides. We only know \(\overline{DE}\parallel\overline{FG}\), no information about \(EF\) and \(GD\) being parallel.
• Rectangle: A rectangle is a parallelogram with four right angles. Since we don't know if it's a parallelogram or has right angles.
• Rhombus: A rhombus is a parallelogram with all sides equal. No information about side - lengths or it being a parallelogram.
• Square: A square is a rectangle and a rhombus. Since we don't have information to confirm it as a rectangle or rhombus.

Answer:

Quadrilateral, Trapezoid