Choose the word "rectangle," "square," or "rhombus" to fill in the blank and make the statement

true. (If none of the words can be used, then write "none.")
A parallelogram is a __________ if and only if its diagonals are perpendicular bisectors of each other.

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To determine which word to choose to fill in the blank, we need to understand the characteristics of each shape mentioned: "rectangle," "square," and "rhombus."

1. Rectangle: A rectangle is a parallelogram with four right angles.

2. Square: A square is a parallelogram with four equal sides and four right angles. It is a special type of rectangle.

3. Rhombus: A rhombus is a parallelogram with four equal sides. Its opposite angles are equal, but they are not necessarily right angles.

The statement says that a parallelogram is a certain shape if and only if its diagonals are perpendicular bisectors of each other. Let's analyze each option:

- Rectangle: In a rectangle, the diagonals are perpendicular bisectors of each other since all angles are right angles. So, a rectangle would make the statement true.

- Square: A square is a special type of rectangle with all sides equal, and all angles are right angles. Therefore, in a square, the diagonals are also perpendicular bisectors of each other. So, a square would also make the statement true.

- Rhombus: In a rhombus, the diagonals bisect each other, meaning they divide each other into equal halves. However, the diagonals are not necessarily perpendicular to each other, except in special cases where the rhombus is also a square. Therefore, a rhombus would not make the statement true.

Based on these explanations, we can conclude that the correct word to fill in the blank is "square."