Suppose that a given parallelogram is not a rhombus or a rectangle. Which of the following can

you conclude about this parallelogram

A) It is a square.
B) Its angles are not all congruent.
C) Its diagonals are perpendicular bisectors of each other.
D) None of the above

To determine the answer, we need to analyze the properties of parallelograms, rhombuses, and rectangles.

1. Parallelogram: A quadrilateral with opposite sides that are parallel.

2. Rhombus: A parallelogram with all sides of equal length.

3. Rectangle: A parallelogram with all angles measuring 90 degrees (right angles).

Since the question states that the given parallelogram is not a rhombus or a rectangle, we can eliminate options A and B:

A) It is a square: A square is a special type of rhombus and rectangle, so if the parallelogram is not a rhombus or a rectangle, it cannot be a square.

B) Its angles are not all congruent: If the parallelogram were a rectangle, all of its angles would be congruent. But since it is stated that the parallelogram is not a rectangle, we cannot conclude that its angles are all congruent.

Now let's consider option C:

C) Its diagonals are perpendicular bisectors of each other: This property is true for rectangles, but not for all parallelograms. Therefore, we cannot conclude this about the given parallelogram either.

Therefore, the correct answer is D) None of the above.