Which of the following statements are true and which are false?
(a) The diagonals of a parallelogram are equal.
(b) The diagonals of a rectangle are perpendicular to each other.
( c) The diagonals of a rhombus are equal.

Answer

To determine whether the statements about the diagonals of various quadrilaterals are true or false, we will analyze each statement step by step.

### Step-by-Step Solution:

1. **Statement (a): The diagonals of a parallelogram are equal.**
- A parallelogram has opposite sides that are equal and parallel. However, the diagonals of a parallelogram are not necessarily equal. They bisect each other but are not equal in length unless the parallelogram is a rectangle. Therefore, this statement is **False**.

2. **Statement (b): The diagonals of a rectangle are perpendicular to each other.**
- A rectangle has all angles equal to 90 degrees, and while the diagonals of a rectangle are equal in length, they are not perpendicular to each other. The diagonals intersect at the midpoint but do not form right angles. Therefore, this statement is **False**.

3. **Statement (c): The diagonals of a rhombus are equal.**
- In a rhombus, all sides are equal, but the diagonals are not equal in length. They bisect each other at right angles, but they are not the same length unless the rhombus is a square. Therefore, this statement is **False**.

### Summary of Results:
- (a) False
- (b) False
- (c) False