A parallelogram must NOT be a rectangle if its diagonals :-

Options

A. Bisect each other
B. Are congruent
C. Are Perpendicular to each other
D. None of these

Answer

To determine which property of the diagonals of a parallelogram must NOT be true for it to be a rectangle, we can analyze the properties of both parallelograms and rectangles.

### Step-by-Step Solution:

1. **Understand the Properties of a Rectangle:**
- A rectangle is a type of parallelogram with specific properties:
- All angles are 90 degrees.
- Opposite sides are equal.
- Diagonals are equal in length.
- Diagonals bisect each other.

2. **List the Given Options:**
- A) Diagonals bisect each other.
- B) Diagonals are congruent (equal).
- C) Diagonals are perpendicular to each other.
- D) None of these.

3. **Analyze Each Option:**
- **Option A:** Diagonals bisect each other.
- This property is true for both rectangles and parallelograms. Therefore, this option does not indicate that the parallelogram is not a rectangle.

- **Option B:** Diagonals are congruent.
- This property is also true for both rectangles and parallelograms. Thus, this option does not indicate that the parallelogram is not a rectangle.

- **Option C:** Diagonals are perpendicular to each other.
- This property is not true for rectangles. While the diagonals of a rectangle bisect each other and are congruent, they are not perpendicular to each other. This property is true for squares, which are a special case of rectangles, but not for rectangles in general.

- **Option D:** None of these.
- This option implies that all previous options could be true for rectangles, which is not the case.

4. **Conclusion:**
- The property that must NOT be true for a parallelogram to be a rectangle is that **diagonals are perpendicular to each other**. Thus, the correct answer is Option C.

### Final Answer:
The parallelogram must NOT be a rectangle if its diagonals are perpendicular to each other.

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