A rectangle is symmetrical about

Options

A. each one of its sides
B. each one of its diagonals
C. a line joining the midpoints of its opposite sides
D. none of these

Answer

To determine the lines of symmetry for a rectangle, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Symmetry**:
- Symmetry in geometry means that one half of a shape is a mirror image of the other half. A line of symmetry divides the shape into two identical parts.

2. **Drawing a Rectangle**:
- Start by drawing a rectangle. For example, let’s label the corners of the rectangle as A, B, C, and D in clockwise order.

3. **Identifying Lines of Symmetry**:
- For a rectangle, we can find the lines of symmetry by considering the midpoints of the sides.
- **Vertical Line of Symmetry**: Draw a vertical line that divides the rectangle into two equal halves. This line goes through the midpoints of the top and bottom sides (AB and CD).
- **Horizontal Line of Symmetry**: Draw a horizontal line that divides the rectangle into two equal halves. This line goes through the midpoints of the left and right sides (AD and BC).

4. **Counting the Lines of Symmetry**:
- From the above, we see that there are two lines of symmetry for a rectangle:
- One vertical line (midpoint of opposite sides).
- One horizontal line (midpoint of opposite sides).

5. **Checking Other Options**:
- **Diagonals**: A rectangle does not have symmetry along its diagonals. If you fold the rectangle along the diagonal, the two halves will not match.
- **Each Side**: A rectangle is not symmetrical about each of its sides individually.
- **None of the Above**: This option is also incorrect since we have identified valid lines of symmetry.

6. **Conclusion**:
- The correct answer is that a rectangle is symmetrical about a line joining the midpoints of its opposite sides.

### Final Answer:
- Therefore, the answer is **Option 3: a line joining the midpoint of its opposite sides**.