Question

choose all answers that describe the polygon ( abcd ) if ( angle a cong angle b, angle c cong angle d ), and ( overline{ab} parallel overline{cd} ).
answer attempt 1 out of 2
parallelogram
quadrilateral
rectangle
rhombus
square
trapezoid

Explanation:

Step1: Recall definitions

A quadrilateral is a four - sided polygon. Since \(ABCD\) has four sides, it is a quadrilateral.
A trapezoid is a quadrilateral with at least one pair of parallel sides. Given \(\overline{AB}\parallel\overline{CD}\), \(ABCD\) is a trapezoid.
For a parallelogram, we need both pairs of opposite sides to be parallel. We only know \(\overline{AB}\parallel\overline{CD}\), no information about \(\overline{AD}\) and \(\overline{BC}\) being parallel.
For a rectangle (a special parallelogram with right angles), we lack information about angles being \(90^{\circ}\) and both pairs of opposite sides parallel.
For a rhombus (a special parallelogram with all sides equal), we have no information about side lengths.
For a square (a special rectangle and rhombus), we lack information about side lengths and angles being \(90^{\circ}\) and both pairs of opposite sides parallel.

Answer:

B. Quadrilateral, F. Trapezoid