Let's analyze each statement step-by-step to determine which ones are true for a square WXYZ:
A. WX = XY
In a square, all four sides are of equal length. Therefore, the length of side WX equals the length of side XY.
- True
B. W is a right angle
In a square, all four interior angles are right angles, meaning they are each 90 degrees.
- True
C. WXYZ is a trapezoid
A trapezoid is defined as a quadrilateral with at least one pair of parallel sides. While a square does have two pairs of parallel sides, the definition of a trapezoid typically suggests it requires exactly one pair. Since a square has two pairs of parallel sides, it is not classified as a trapezoid.
- False
D. ZW is congruent to Y
Congruency in geometry means that two figures have the same shape and size. ZW represents a side (a length), while Y represents an angle. An angle and a length cannot be congruent to each other.
- False
E. ZW is supplementary to Y
Supplementary means that two angles add up to 180 degrees. Here, ZW is a side (a length), and Y is an angle. Since a length and an angle cannot be added together to make 180 degrees, they cannot be supplementary.
- False
F. WXYZ is a parallelogram
A parallelogram is defined as a quadrilateral with both pairs of opposite sides parallel. A square fits this definition as it has both pairs of opposite sides parallel and equal.
- True
Given the analysis:
- WX = XY: True
- W is a right angle: True
- WXYZ is a trapezoid: False
- ZW is congruent to Y: False
- ZW is supplementary to Y: False
- WXYZ is a parallelogram: True
Therefore, the statements that must be true are:
- A. WX = XY
- B. W is a right angle
- F. WXYZ is a parallelogram
