Let's examine each statement one by one:

A. If one interior angle of a parallelogram is a right angle, then the parallelogram must be a rectangle.

• Correct. In a parallelogram, opposite angles are equal, and adjacent angles are supplementary (they add up to 180°). If one angle is a right angle (90°), then all the other angles must also be right angles. Therefore, the parallelogram is a rectangle, as rectangles are defined as parallelograms with all right angles.

B. If two diagonals of a rectangle are perpendicular, then the rectangle must be a square.

• Incorrect. A rectangle has perpendicular diagonals only in the special case when it is a square. In a general rectangle, the diagonals are not perpendicular, and the property of perpendicular diagonals is characteristic of rhombuses and squares.

C. If two diagonals of a rhombus are equal, then the rhombus must be a square.

• Correct. In a rhombus, the diagonals are perpendicular and bisect each other at right angles. If the diagonals are also equal in length, the rhombus must be a square because a square is a special type of rhombus where all angles are 90° and the diagonals are both equal and perpendicular.

D. If one interior angle of a rhombus is a right angle, then the rhombus must be a square.

• Correct. If one interior angle of a rhombus is a right angle, all four angles must be right angles because in a rhombus, opposite angles are equal and adjacent angles are supplementary. If the angles are all 90°, the rhombus is a square.

E. If two diagonals of a kite are equal, then the kite must be a square.

• Incorrect. A kite has two pairs of adjacent sides that are equal in length, but its diagonals are generally not equal. The diagonals of a kite are only equal in length in the special case where the kite is a square, but this is not a general property of kites.

F. If two diagonals of a parallelogram are equal, then the parallelogram must be a rectangle.

• Correct. In a parallelogram, if the diagonals are equal, it implies that the parallelogram is a rectangle. This is because only rectangles and squares (which are a type of rectangle) have diagonals that are of equal length in general parallelograms.

Summary of Correctness:

• A. Correct
• B. Incorrect
• C. Correct
• D. Correct
• E. Incorrect
• F. Correct

---

Would you like more details or have any specific questions about the reasoning behind these statements? Here are five additional questions to explore this topic further:

1. What is the difference between a rhombus and a square in terms of their properties?
2. Why do the diagonals of a rectangle not necessarily have to be perpendicular?
3. Can a parallelogram have equal diagonals without being a rectangle? If so, what would that shape be?
4. How does the property of diagonals in a kite differ from that in a rhombus or square?
5. What is the relationship between the angles and diagonals of a parallelogram, and how do they help determine the shape?

Tip: When studying geometric properties, it's helpful to sketch the figures and label key features (such as angles and diagonals) to visually understand why certain statements are true or false.