In a parallelogram, the diagonals are equal ( T / F )

Answer

To determine whether the statement "In a parallelogram, the diagonals are equal" is true or false, we can analyze the properties of parallelograms and their diagonals.

### Step-by-Step Solution:

1. **Understanding Parallelograms**:
A parallelogram is a four-sided figure (quadrilateral) where opposite sides are parallel and equal in length.

2. **Properties of Diagonals in Parallelograms**:
In general, the diagonals of a parallelogram bisect each other. This means that they cut each other into two equal parts, but this does not necessarily mean that the diagonals themselves are equal.

3. **Special Cases**:
The diagonals of a parallelogram are equal only in specific cases:
- When the parallelogram is a rectangle (where all angles are 90 degrees).
- When the parallelogram is a square (which is a special case of a rectangle).

4. **Conclusion**:
Since not all parallelograms have equal diagonals (for example, a rhombus has diagonals that are not equal), the statement "In a parallelogram, the diagonals are equal" is **False**.

### Final Answer:
**False** - In a parallelogram, the diagonals are not equal except in the special cases of rectangles and squares.

---