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

### Step 1: Understand the Concept of 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, the lines of symmetry can be drawn through the vertices and midpoints of the sides.

**Hint:** Think about how many ways you can fold the polygon so that both halves match perfectly.

### Step 2: Analyze Different Regular Polygons
Let's consider a few examples of regular polygons:
- **Triangle (3 sides)**: A triangle has 3 lines of symmetry. Each line can be drawn from a vertex to the midpoint of the opposite side.
- **Square (4 sides)**: A square has 4 lines of symmetry. These include two vertical and horizontal lines, as well as two diagonal lines.
- **Pentagon (5 sides)**: A regular pentagon has 5 lines of symmetry, with each line going from a vertex to the midpoint of the opposite side.

**Hint:** Draw the polygons and try to identify the lines of symmetry visually.

### Step 3: Generalize the Pattern
From the examples above, we can see that for any regular polygon with \( n \) sides, there are exactly \( n \) lines of symmetry. This is because:
- Each vertex can connect to the midpoint of the opposite side, creating a line of symmetry.
- Additionally, lines can be drawn through the midpoints of opposite sides.

**Hint:** Consider how the symmetry works for polygons with more sides. Does the pattern hold?

### Step 4: Conclusion
Thus, we conclude that for a regular polygon with \( n \) sides, the number of lines of symmetry 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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