Question

question 16 of 25 if wxyz is a square, which statements must be true? check all that apply. a. wxyz is a rhombus. b. $overline{wx}$ is perpendicular to $overline{xy}$. c. $angle w$ is congruent to $angle x$. d. wxyz is a trapezoid. e. $angle w$ is supplementary to $angle x$. f. $overline{wx}$ is parallel to $overline{yz}$

Explanation:

Step1: Recall properties of a square

A square has all sides equal, all angles equal to 90 degrees, opposite - sides parallel.

Step2: Analyze option A

A rhombus has all sides equal. Since a square has all sides equal, a square is a special - type of rhombus. So, if \(WXYZ\) is a square, it is a rhombus.

Step3: Analyze option B

In a square, adjacent sides are perpendicular. So, \(\overline{WX}\) is perpendicular to \(\overline{XY}\).

Step4: Analyze option C

In a square, all angles are 90 degrees. So, \(\angle W=\angle X = 90^{\circ}\), and \(\angle W\) is congruent to \(\angle X\).

Step5: Analyze option D

A trapezoid has exactly one pair of parallel sides. A square has two pairs of parallel sides, so it is not a trapezoid.

Step6: Analyze option E

In a square, \(\angle W=\angle X = 90^{\circ}\), and \(90^{\circ}+90^{\circ}=180^{\circ}\). So, \(\angle W\) is supplementary to \(\angle X\).

Step7: Analyze option F

In a square, opposite sides are parallel. So, \(\overline{WX}\) is parallel to \(\overline{YZ}\).

Answer:

A. \(WXYZ\) is a rhombus.
B. \(\overline{WX}\) is perpendicular to \(\overline{XY}\).
C. \(\angle W\) is congruent to \(\angle X\).
E. \(\angle W\) is supplementary to \(\angle X\).
F. \(\overline{WX}\) is parallel to \(\overline{YZ}\)