Question

choose all answers that describe the quadrilateral abcd if $overline{ab}paralleloverline{cd}$, $overline{ab}congoverline{cd}$, diagonal $overline{ac}$ bisects $angle a$ and $angle c$, and diagonal $overline{bd}$ bisects $angle b$ and $angle d$. answer attempt 1 out of 2 parallelogram rectangle rhombus square trapezoid

Explanation:

Step1: Recall parallelogram - definition

If one pair of opposite sides of a quadrilateral is parallel and congruent ($\overline{AB}\parallel\overline{CD}$ and $\overline{AB}\cong\overline{CD}$), then the quadrilateral $ABCD$ is a parallelogram.

Step2: Recall rhombus - property

In a parallelogram, if the diagonals bisect the angles of the parallelogram (diagonal $\overline{AC}$ bisects $\angle A$ and $\angle C$, and diagonal $\overline{BD}$ bisects $\angle B$ and $\angle D$), then the parallelogram is a rhombus.

Step3: Analyze rectangle - condition

For a rectangle, the diagonals are equal in length and bisect each other, but there is no information about the equality of diagonals here, so it may not be a rectangle.

Step4: Analyze square - condition

A square is a special - case of a rhombus with all angles equal to 90 degrees. There is no information about the angles being 90 degrees, so it may not be a square.

Step5: Analyze trapezoid - condition

A trapezoid has only one pair of parallel sides. Since we have a parallelogram (two pairs of parallel sides), it is not a trapezoid.

Answer:

Parallelogram, Rhombus