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Answer :
To determine which statements must be true for the square WXYZ, let's go through each option one by one:
A. WXYZ is a parallelogram.
- A square is a specific type of quadrilateral where all sides are equal, and all angles are right angles. A square also meets the criteria of a parallelogram because its opposite sides are parallel and equal in length. Therefore, WXYZ as a square is indeed a parallelogram.
- True
B. W is congruent to Y.
- In any square, all angles are equal. Therefore, angle W is congruent to angle Y since both are right angles (90 degrees).
- True
C. W is supplementary to angle Y.
- Supplementary angles are two angles that add up to 180 degrees. Since angle W and angle Y in a square are each 90 degrees, their sum is indeed 180 degrees. This makes them supplementary.
- True
D. W is a right angle.
- In a square, each of the four angles is a right angle, which is 90 degrees. So, angle W, being one of those angles, is a right angle.
- True
E. WXYZ is a trapezoid.
- A trapezoid is defined as a quadrilateral with at least one pair of parallel sides. While a square has two pairs of parallel sides, it is not classified as a trapezoid but as a parallelogram and a rectangle. Therefore, it does not meet the definition of a trapezoid for this context.
- False
F. WX = XY
- In a square, all four sides are equal in length. So the side WX is equal to side XY.
- True
Thus, the statements that must be true for the square WXYZ are A, B, C, D, and F.
A. WXYZ is a parallelogram.
- A square is a specific type of quadrilateral where all sides are equal, and all angles are right angles. A square also meets the criteria of a parallelogram because its opposite sides are parallel and equal in length. Therefore, WXYZ as a square is indeed a parallelogram.
- True
B. W is congruent to Y.
- In any square, all angles are equal. Therefore, angle W is congruent to angle Y since both are right angles (90 degrees).
- True
C. W is supplementary to angle Y.
- Supplementary angles are two angles that add up to 180 degrees. Since angle W and angle Y in a square are each 90 degrees, their sum is indeed 180 degrees. This makes them supplementary.
- True
D. W is a right angle.
- In a square, each of the four angles is a right angle, which is 90 degrees. So, angle W, being one of those angles, is a right angle.
- True
E. WXYZ is a trapezoid.
- A trapezoid is defined as a quadrilateral with at least one pair of parallel sides. While a square has two pairs of parallel sides, it is not classified as a trapezoid but as a parallelogram and a rectangle. Therefore, it does not meet the definition of a trapezoid for this context.
- False
F. WX = XY
- In a square, all four sides are equal in length. So the side WX is equal to side XY.
- True
Thus, the statements that must be true for the square WXYZ are A, B, C, D, and F.
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