Lines of Symmetry for Regular Polygons A regular polygon is a polygon with n sides, where n is an integer greater than 2. A line of symmetry is a line that...
Lines of Symmetry for Regular Polygons
A regular polygon is a polygon with n sides, where n is an integer greater than 2. A line of symmetry is a line that divides the polygon into two congruent halves. Regular polygons have an infinite number of lines of symmetry, each passing through the center of the polygon.
These lines of symmetry are perpendicular to the sides of the polygon and are equally spaced. They intersect the center of the polygon at angles of 120 degrees.
The lines of symmetry are also perpendicular to the interior angles of the polygon. This is because the interior angles of a regular polygon are equal to 120 degrees, and the lines of symmetry bisect these angles.
The number of lines of symmetry of a regular polygon is equal to n. This is because a line of symmetry divides the polygon into two congruent halves, and each half contains n/2 vertices.
Examples of regular polygons with different numbers of sides are shown below:
A triangle has 3 lines of symmetry.
A square has 4 lines of symmetry.
A regular hexagon has 6 lines of symmetry.
A regular heptagon has 7 lines of symmetry.
A regular octagon has 8 lines of symmetry.
A regular n-gon has n lines of symmetry