A regular decagon is a ten-sided polygon where all sides and angles are equal. One of the fascinating properties of regular polygons is their lines of symmetry, which are the lines that can be drawn through the shape such that one side mirrors the other.
For a regular decagon, there are two types of lines of symmetry:
- Vertex Symmetry Lines: These lines run from one vertex of the decagon to the midpoint of the opposite side. Since a decagon has 10 vertices, you can draw these types of lines from each vertex, resulting in 10 lines.
- Side Symmetry Lines: These lines run through the midpoints of two opposite sides. A regular decagon has 10 sides, which allows for another 5 lines of symmetry when drawn between two opposing sides.
Adding these together, a regular decagon has a total of 10 (vertex lines) + 5 (side lines) = 15 lines of symmetry.
This symmetry is one of the reasons why regular decagons are often used in design and architecture, as their balanced appearance creates an aesthetically pleasing visual alignment.