The diagonals of a parallelogram are equal.

Options

A. true
B. false
C. can not say anything
D. none of these

Answer

To determine whether the statement "The diagonals of a parallelogram are equal" is true or false, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Parallelogram Properties**:
A parallelogram is a quadrilateral with opposite sides that are equal and parallel. The properties of a parallelogram include that its opposite angles are equal, and the diagonals bisect each other.

**Hint**: Remember the basic properties of a parallelogram, especially how the sides and angles relate to each other.

2. **Drawing the Parallelogram**:
Let's draw a parallelogram ABCD. Label the vertices as A, B, C, and D in a clockwise direction. The diagonals are AC and BD.

**Hint**: Visualize the shape by sketching it out, as it helps in understanding the relationships between the sides and diagonals.

3. **Identifying the Diagonals**:
The diagonals of the parallelogram are AC and BD. We need to analyze their lengths.

**Hint**: Mark the diagonals clearly in your drawing to see how they intersect.

4. **Diagonals Bisect Each Other**:
In a parallelogram, the diagonals bisect each other at a point O. This means that AO = OC and BO = OD.

**Hint**: Use the midpoint concept to understand how the diagonals divide each other.

5. **Congruent Triangles**:
To prove that the diagonals are not equal, we can consider triangles AOB and COD. Since AO = OC and BO = OD, we can use the Side-Angle-Side (SAS) postulate to show that triangles AOB and COD are congruent.

**Hint**: Remember that congruent triangles have equal corresponding sides and angles.

6. **Conclusion About Diagonal Lengths**:
Since the diagonals bisect each other but are not equal in length, we conclude that the diagonals of a parallelogram are not equal. Therefore, the statement "The diagonals of a parallelogram are equal" is false.

**Hint**: Summarize your findings clearly to reinforce your conclusion.

### Final Conclusion:
The statement "The diagonals of a parallelogram are equal" is **False**.