The diagonals of a square are perpendicular to one another.

Answer

To determine whether the statement "The diagonals of a square are perpendicular to one another" is true, we can analyze the properties of a square and its diagonals step by step.

### Step-by-Step Solution:

1. **Understanding the Square:**
- A square is a four-sided polygon (quadrilateral) with all sides equal in length and all angles equal to 90 degrees.

**Hint:** Remember that a square has equal sides and right angles.

2. **Identifying the Diagonals:**
- A square has two diagonals. These are the lines that connect opposite corners (vertices) of the square.

**Hint:** Diagonals are drawn from one vertex to the opposite vertex.

3. **Properties of Diagonals in a Square:**
- In a square, the diagonals not only connect opposite vertices but also have some special properties:
- They are equal in length.
- They bisect each other (they cut each other in half).

**Hint:** Think about how the diagonals divide the square into two equal triangles.

4. **Checking Perpendicularity:**
- To check if the diagonals are perpendicular, we need to see if they intersect at a right angle (90 degrees).
- When you draw the diagonals of a square, they intersect at the center of the square.

**Hint:** Visualize or draw the square and its diagonals to see the angles formed.

5. **Conclusion:**
- Since the diagonals of a square intersect at the center and form right angles (90 degrees) with each other, we conclude that the diagonals of a square are indeed perpendicular to one another.

**Hint:** Remember that perpendicular lines meet at a right angle.

### Final Answer:
The statement "The diagonals of a square are perpendicular to one another" is true.