Question

question
choose all answers that describe the quadrilateral defg if m∠d = m∠e = m∠f = m∠g, diagonal (overline{df}) bisects ∠d and ∠f, and diagonal (overline{eg}) bisects ∠e and ∠g.
answer
attempt 1 out of 2
□ parallelogram
□ rectangle
□ rhombus
□ square
□ trapezoid

Explanation:

Step1: Recall angle - sum property of quadrilaterals

The sum of interior angles of a quadrilateral is $360^{\circ}$. Since $\text{m}\angle D=\text{m}\angle E=\text{m}\angle F=\text{m}\angle G$, then $\text{m}\angle D=\text{m}\angle E=\text{m}\angle F=\text{m}\angle G = 90^{\circ}$. A quadrilateral with all angles equal to $90^{\circ}$ is a rectangle.

Step2: Recall angle - bisecting property

The diagonal $\overline{DF}$ bisects $\angle D$ and $\angle F$, and diagonal $\overline{EG}$ bisects $\angle E$ and $\angle G$. In a rectangle, when the diagonals bisect the angles, the rectangle is a square. A square is also a parallelogram and a rhombus. A parallelogram has opposite - sides parallel, a rhombus has all sides equal, and a square has all the properties of a parallelogram, rectangle, and rhombus. A trapezoid has only one pair of parallel sides, which is not the case here.

Answer:

A. Parallelogram
B. Rectangle
C. Rhombus
D. Square