The diagonals of a quadrilateral bisect each other. This quadrilateral is a

Options

A. rectangle
B. kite
C. trapezium
D. none of these

Answer

To solve the question, "The diagonals of a quadrilateral bisect each other. This quadrilateral is a:", we need to analyze the properties of the given options.

### Step-by-Step Solution:

1. **Understanding the Question**: We need to identify which type of quadrilateral has the property that its diagonals bisect each other.

2. **Analyzing Option A - Rectangle**:
- A rectangle is a quadrilateral with opposite sides equal and all angles equal to 90 degrees.
- In a rectangle, the diagonals are equal in length and bisect each other.
- Therefore, this option satisfies the condition.

3. **Analyzing Option B - Kite**:
- A kite is a quadrilateral with two pairs of adjacent sides that are equal.
- In a kite, the diagonals are not equal, and only one of the diagonals bisects the other.
- Therefore, this option does not satisfy the condition.

4. **Analyzing Option C - Trapezium**:
- A trapezium (or trapezoid in some regions) is a quadrilateral with at least one pair of parallel sides.
- The diagonals of a trapezium do not necessarily bisect each other.
- Therefore, this option does not satisfy the condition.

5. **Analyzing Option D - None of These**:
- Since we have already identified that a rectangle meets the criteria, this option is incorrect.

6. **Conclusion**: The only quadrilateral among the options whose diagonals bisect each other is a rectangle.

### Final Answer:
The quadrilateral whose diagonals bisect each other is a **rectangle**.

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