High School

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If \( wxyz \) is a square, which statements must be true? Check all that apply.

A. \( \angle w \) is a right angle.
B. \( w \) is congruent to \( zy \).
C. \( wxyz \) is a trapezoid.
D. \( w \) is supplementary to \( zy \).
E. \( wxyz \) is a parallelogram.

Answer :

The true statements about the square wxyz are :
a. w is a right angle,
b. w is congruent to z
d. w is supplementary to z
e. wxyz is a parallelogram.

Let us analyze each statement based on the properties of a square:

  1. W is a right angle. This is true because all interior angles in a square are right angles (90 degrees).
  2. W is congruent to ZY. This is true because all sides of a square are congruent (equal in length).
  3. WXYZ is a trapezoid. This is false. A square is not classified as a trapezoid because a trapezoid only has one pair of parallel sides, whereas a square has two pairs of parallel sides.
  4. W is supplementary to ZY. This is true. Supplementary angles add up to 180 degrees. In a square, any two adjacent interior angles are supplementary because they each measure 90 degrees.
  5. WXYZ is a parallelogram. This is true because all squares are parallelograms, as both pairs of opposite sides are parallel.

Therefore, the following statements must be true: a, b, d, and e.

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