For which of the following , diagonals are equal?

Options

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

Answer

To determine which of the following quadrilaterals have equal diagonals, we can analyze each shape one by one. The options typically include trapezium, rhombus, parallelogram, and rectangle.

### Step-by-Step Solution:

1. **Trapezium**:
- A trapezium has one pair of opposite sides that are parallel.
- The diagonals of a trapezium are not equal in length.
- **Conclusion**: Diagonals are not equal.

2. **Rhombus**:
- A rhombus is a type of parallelogram where all sides are equal in length.
- The diagonals of a rhombus bisect each other at right angles, but they are not equal in length.
- **Conclusion**: Diagonals are not equal.

3. **Parallelogram**:
- In a parallelogram, opposite sides are equal and parallel.
- The diagonals of a parallelogram are not necessarily equal; they can be of different lengths.
- **Conclusion**: Diagonals are not equal.

4. **Rectangle**:
- A rectangle is a specific type of parallelogram where all angles are right angles (90 degrees).
- In a rectangle, the diagonals are equal in length. This can be proven using the Pythagorean theorem, as the diagonals act as the hypotenuse of two right triangles formed by the sides of the rectangle.
- **Conclusion**: Diagonals are equal.

### Final Conclusion:
Among the given quadrilaterals, only the **rectangle** has equal diagonals.