How many lines of symmetry does each of the following shapes have? a) A square b) A regular pentagon c) A regular hexagon d) A regular 20-sided polygon
The Correct Answer and Explanation is:
Let’s analyze each shape:
a) Square:
A square has 4 lines of symmetry. These lines of symmetry are as follows:
- Two diagonals that connect opposite corners.
- Two lines that bisect the square horizontally and vertically through the midpoints of the sides.
A square is a type of rectangle where all sides are equal, and it has symmetry in multiple directions: vertically, horizontally, and diagonally.
b) Regular Pentagon:
A regular pentagon has 5 lines of symmetry. These lines pass through:
- Each vertex and the midpoint of the opposite side. There are five vertices and five corresponding midpoints of the opposite sides, meaning there are five lines of symmetry.
Each line of symmetry cuts the pentagon in half, making the two halves mirror images of each other. The symmetry is also linked to the rotational symmetry of a regular pentagon, where you can rotate the pentagon by multiples of 72° (360°/5).
c) Regular Hexagon:
A regular hexagon has 6 lines of symmetry. These lines can be described as:
- Three lines passing through opposite vertices.
- Three lines that bisect the sides of the hexagon, running through the midpoints of opposite sides.
The symmetry of a regular hexagon is related to its rotational symmetry, where you can rotate it by multiples of 60° (360°/6) and still have the same shape.
d) Regular 20-sided Polygon (Icosagon):
A regular 20-sided polygon, or icosagon, has 20 lines of symmetry. These lines of symmetry pass through:
- Each vertex and the midpoint of the opposite side. Since the polygon has 20 sides and vertices, there are 20 such lines of symmetry.
The icosagon has a high degree of rotational symmetry; you can rotate it by multiples of 18° (360°/20) and the shape will still align perfectly.
Conclusion:
The number of lines of symmetry for each shape is as follows:
- Square: 4
- Regular Pentagon: 5
- Regular Hexagon: 6
- Regular 20-sided Polygon: 20
