Question

if wxyz is a square, which statements must be true? check all that apply. a. ∠w is congruent to ∠x. b. wxyz is a rhombus. c. wx is perpendicular to xy. d. wx is parallel to yz. e. wxyz is a trapezoid. f. ∠w is supplementary to ∠x

Explanation:

Step1: Recall properties of a square

A square has all - right angles, all sides equal, opposite sides parallel, and adjacent sides perpendicular.

Step2: Analyze option A

In a square, all angles are right - angles. So, $\angle W = \angle X=90^{\circ}$, and $\angle W$ is congruent to $\angle X$.

Step3: Analyze option B

A square is a special type of rhombus with all angles equal to $90^{\circ}$. A rhombus has all sides equal, and a square has all sides equal and right - angles, so a square is a rhombus.

Step4: Analyze option C

Adjacent sides of a square are perpendicular. So, $\overline{WX}$ is perpendicular to $\overline{XY}$.

Step5: Analyze option D

Opposite sides of a square are parallel. So, $\overline{WX}$ is parallel to $\overline{YZ}$.

Step6: Analyze option E

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

Step7: Analyze option F

Since $\angle W=\angle X = 90^{\circ}$, $\angle W+\angle X=180^{\circ}$, so $\angle W$ is supplementary to $\angle X$.

Answer:

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