Question

choose all answers that describe the polygon efgh if m∠e = m∠f, m∠g = m∠h, and (overline{ef}paralleloverline{gh}). answer attempt 2 out of 3 parallelogram quadrilateral rectangle rhombus square trapezoid

Explanation:

Step1: Recall polygon definitions

A polygon with 4 sides is a quadrilateral. Since $EFGH$ has 4 vertices, it is a quadrilateral.

Step2: Analyze parallel - side condition

Given $\overline{EF}\parallel\overline{GH}$, a polygon with one pair of parallel sides is a trapezoid.

Step3: Analyze angle - equality conditions

Just because $\angle E=\angle F$ and $\angle G = \angle H$, we cannot be sure it is a parallelogram (for a parallelogram, we need both pairs of opposite sides parallel or both pairs of opposite angles equal in a more general sense related to parallel - side properties), rectangle (needs right - angles), rhombus (needs equal - side lengths), or square (needs equal - side lengths and right - angles).

Answer:

Quadrilateral, Trapezoid