For which of the following figures, diagonals are perpendicular to each other?

Options

A. Parallelogram
B. Kite
C. Trapezium
D. Rectangle

Answer

To determine which of the given figures has diagonals that are perpendicular to each other, we will analyze each figure step by step.

### Step-by-Step Solution:

1. **Identify the Figures**:
We need to consider the following figures: Parallelogram, Trapezium, Rectangle, and Kite.

2. **Analyze the Parallelogram**:
- In a parallelogram, the diagonals bisect each other.
- However, they do not intersect at right angles (90 degrees).
- **Conclusion**: The diagonals of a parallelogram are not perpendicular.

3. **Analyze the Trapezium**:
- In a trapezium, the diagonals do not bisect each other.
- They also do not intersect at right angles.
- **Conclusion**: The diagonals of a trapezium are not perpendicular.

4. **Analyze the Rectangle**:
- In a rectangle, the diagonals bisect each other and are equal in length.
- However, they do not intersect at right angles.
- **Conclusion**: The diagonals of a rectangle are not perpendicular.

5. **Analyze the Kite**:
- In a kite, one diagonal bisects the other.
- The diagonals of a kite intersect at right angles (90 degrees).
- To prove this, consider the two triangles formed by the diagonals. The sides of the kite are equal, and the angles formed at the intersection are congruent due to the properties of isosceles triangles.
- **Conclusion**: The diagonals of a kite are perpendicular to each other.

### Final Answer:
The figure for which the diagonals are perpendicular to each other is the **Kite**.

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