Question

question 9 of 25
if wxyz is a square, which statements must be true? check all that apply.
a. wxyz is a rectangle.
b. wxyz is a rhombus.
c. (overline{wx}congoverline{yz})
d. (overline{wx}congoverline{xy})
e. (angle w) is a right angle.
f. wxyz is a trapezoid.

Explanation:

Step1: Recall properties of a square

A square has all the properties of a rectangle (opposite sides are equal and parallel, all angles are right angles), a rhombus (all sides are equal), and a parallelogram.

Step2: Analyze option A

By definition, a square is a special type of rectangle where all sides are equal. So if WXYZ is a square, it is a rectangle.

Step3: Analyze option B

A square is a special type of rhombus where all angles are right angles. So if WXYZ is a square, it is a rhombus.

Step4: Analyze option C

In a square, opposite sides are congruent. So $\overline{WX}\cong\overline{YZ}$.

Step5: Analyze option D

In a square, all four sides are congruent. So $\overline{WX}\cong\overline{XY}$.

Step6: Analyze option E

All angles in a square are right - angles, so $\angle W = 90^{\circ}$.

Step7: Analyze option F

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

Answer:

A. WXYZ is a rectangle.
B. WXYZ is a rhombus.
C. $\overline{WX}\cong\overline{YZ}$
D. $\overline{WX}\cong\overline{XY}$
E. $\angle W$ is a right - angle.