For which of the following, diagonals bisect each other?

Options

A. Square
B. Kite
C. Trapezium
D. Quadrilateral

Answer

To determine which of the given quadrilaterals has diagonals that bisect each other, we will analyze each option step by step.

### Step-by-Step Solution:

1. **Understanding Quadrilaterals**:
A quadrilateral is a four-sided figure. It can be of various types, but we need to focus on the properties of their diagonals.

**Hint**: Remember that diagonals are the line segments connecting non-adjacent vertices of a polygon.

2. **Analyzing the Quadrilateral**:
A general quadrilateral does not have any specific properties regarding the diagonals. The diagonals may or may not bisect each other.

**Hint**: Think about whether all quadrilaterals share any common diagonal properties.

3. **Analyzing the Trapezium**:
A trapezium has one pair of parallel sides. The diagonals of a trapezium do not necessarily bisect each other.

**Hint**: Consider the definition of a trapezium and how its sides affect the diagonals.

4. **Analyzing the Kite**:
A kite has two pairs of adjacent sides that are equal. In a kite, only one diagonal bisects the other, while the other diagonal does not bisect.

**Hint**: Recall the properties of the diagonals in a kite and how they interact.

5. **Analyzing the Rhombus**:
A rhombus is a special type of parallelogram where all sides are equal. In a rhombus, the diagonals bisect each other at right angles.

**Hint**: Think about the properties of parallelograms and how they apply to a rhombus.

6. **Conclusion**:
Among the options given:
- Quadrilateral: No
- Trapezium: No
- Kite: No (only one diagonal bisects)
- Rhombus: Yes (both diagonals bisect each other)

Therefore, the answer is that the **Rhombus** is the quadrilateral whose diagonals always bisect each other.