A quadrilateral whose all sides are equal, opposite angles are equal and the diagonals bisect each other at right angles is a __________.

Options

A. rhombus
B. parallelogram
C. square
D. rectangle

Answer

To solve the question, "A quadrilateral whose all sides are equal, opposite angles are equal and the diagonals bisect each other at right angles is a __________," we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Properties of the Quadrilateral**:
- We know that the quadrilateral has all sides equal, which means it could be a rhombus or a square.
- The opposite angles are equal, which is also a property of both squares and rhombuses.
- The diagonals bisect each other at right angles, which is a specific property of a rhombus.

2. **Identify the Characteristics**:
- In a square, not only do the diagonals bisect each other at right angles, but they are also equal in length.
- In a rhombus, the diagonals bisect each other at right angles, but they are not necessarily equal.

3. **Analyze the Given Conditions**:
- Since the question specifies that the diagonals bisect each other at right angles and does not mention that they are equal, we can conclude that the quadrilateral is a rhombus.

4. **Final Conclusion**:
- Therefore, the answer to the question is: "A quadrilateral whose all sides are equal, opposite angles are equal, and the diagonals bisect each other at right angles is a **rhombus**."