Question

choose all answers that describe the quadrilateral uvwx if $overline{uv}paralleloverline{wx}$, $overline{vw}paralleloverline{xu}$, $uw = vx$, and diagonals are perpendicular: $overline{uw}perpoverline{vx}$. answer attempt 2 out of 2 parallelogram rectangle rhombus square trapezoid

Explanation:

Step1: Recall parallelogram definition

A quadrilateral with opposite - sides parallel is a parallelogram. Since $\overline{UV}\parallel\overline{WX}$ and $\overline{VW}\parallel\overline{XU}$, $UVWX$ is a parallelogram.

Step2: Recall rectangle property

A rectangle has equal diagonals but its diagonals are not necessarily perpendicular. Here, diagonals $\overline{UW}\perp\overline{VX}$, so it may not be a rectangle.

Step3: Recall rhombus property

A rhombus has perpendicular diagonals. Since $\overline{UW}\perp\overline{VX}$ and it is a parallelogram, it could be a rhombus.

Step4: Recall square property

A square is a parallelogram with equal diagonals and perpendicular diagonals. Since $\overline{UW}=\overline{VX}$ and $\overline{UW}\perp\overline{VX}$ and it is a parallelogram, it could be a square.

Step5: Recall trapezoid definition

A trapezoid has only one pair of parallel sides. Here two pairs of sides are parallel, so it is not a trapezoid.

Answer:

A. Parallelogram
C. Rhombus
D. Square