If the diagonals of a quadrilateral are equal and bisect each other at right angles, then the quadrilateral is a

Options

A. reactangle
B. square
C. rhombus
D. trapezium

Answer

To determine the type of quadrilateral where the diagonals are equal and bisect each other at right angles, we can analyze the properties of different quadrilaterals.

### Step-by-Step Solution:

1. **Understanding the Properties of Quadrilaterals**:
- A quadrilateral is a four-sided polygon. The properties of its diagonals can help us identify its type.

2. **Given Conditions**:
- The diagonals of the quadrilateral are equal.
- The diagonals bisect each other at right angles (90 degrees).

3. **Analyzing Each Option**:
- **Rectangle**:
- In a rectangle, the diagonals are equal, but they do not bisect each other at right angles. Thus, a rectangle cannot be the answer.
- **Rhombus**:
- In a rhombus, the diagonals bisect each other at right angles, but they are not equal. Hence, a rhombus cannot be the answer.
- **Trapezium**:
- In a trapezium, the diagonals are not necessarily equal unless it is an isosceles trapezium, and even then, they do not bisect each other at right angles. Therefore, a trapezium cannot be the answer.
- **Square**:
- In a square, the diagonals are equal and they bisect each other at right angles. This satisfies both conditions given in the question.

4. **Conclusion**:
- Since the only quadrilateral that meets both conditions (equal diagonals and diagonals bisecting at right angles) is a square, we conclude that the quadrilateral is a square.

### Final Answer:
The quadrilateral is a **square**.

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