If the number of sides of a regular polygon is n, then the number of lines of symmetry is equal to

Options

A. 2n
B. n
C. `(n)/(2)`
D. `n^(2)`

Answer

To determine the number of lines of symmetry in a regular polygon with \( n \) sides, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Lines of Symmetry**:
A line of symmetry is a line that divides a shape into two identical parts that are mirror images of each other. For regular polygons, these lines can pass through vertices or the midpoints of sides.

2. **Identifying the Regular Polygon**:
A regular polygon is defined as a polygon with all sides and angles equal. Examples include an equilateral triangle, a square, and a regular pentagon.

3. **Counting Lines of Symmetry**:
- For a regular triangle (3 sides), there are 3 lines of symmetry. Each line passes through a vertex and the midpoint of the opposite side.
- For a square (4 sides), there are 4 lines of symmetry. Two lines pass through opposite vertices, and two lines pass through the midpoints of opposite sides.
- For a regular pentagon (5 sides), there are 5 lines of symmetry. Each line passes through a vertex and the midpoint of the opposite side.

4. **Generalizing the Pattern**:
From the examples above, we can see that for any regular polygon with \( n \) sides, there are \( n \) lines of symmetry. This is because:
- Each vertex can be connected to the midpoint of the opposite side, and there are \( n \) vertices in total.
- Additionally, lines can be drawn through the midpoints of opposite sides, but since it’s a regular polygon, the symmetry remains consistent with the number of sides.

5. **Conclusion**:
Therefore, the number of lines of symmetry in a regular polygon with \( n \) sides is equal to \( n \).

### Final Answer:
The number of lines of symmetry in a regular polygon with \( n \) sides is \( n \).

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