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If WXYZ is a square, which statements must be true? Check all that apply.

A. WXYZ is a parallelogram.
B. ∠W is congruent to ∠Y.
C. ∠W is supplementary to ∠Y.
D. ∠W is a right angle.
E. WXYZ is a trapezoid.
F. WX = XY

Answer :

Let's determine which statements must be true if WXYZ is a square:

A. WXYZ is a parallelogram.
A square is a type of rectangle and a specific type of parallelogram. All sides are equal, and opposite sides are parallel, which are the characteristics of a parallelogram.
True

B. W is congruent to Y.
In a square, all angles are congruent because they each measure 90 degrees. So, angle W is congruent to angle Y.
True

C. W is supplementary to \
Supplementary angles add up to 180 degrees. Since each angle in a square is 90 degrees, angle W and angle Y together form 180 degrees. However, in a square, one angle is not supplementary to the other in terms of their relationship to each other, as they are both right angles.
False

D. W is a right angle.
All angles in a square are right angles, meaning they each measure 90 degrees.
True

E. WXYZ is a trapezoid.
A trapezoid has at least one pair of opposite sides that are parallel, but not all sides have to be equal. A square has all sides equal and two pairs of parallel sides, so it's not typically classified as a trapezoid.
False

F. WX = XY
All sides of a square are equal, so side WX is equal to side XY.
True

To summarize, the true statements are A, B, D, and F.

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