Diagonals of Polygons

Diagonals of Polygons

Diagonals are lines that connect the vertices of a polygon. However, segments that connect adjacent vertices are not called diagonal.
A triangle has no diagonal because all vertices are adjacent to each other. The rectangle can draw two lines. The pentagon can draw five lines.

If the number of vertices of the polygon is n, the number of diagonal lines that can be drawn is as follows.

\[ diagonal \, lines = \frac { n(n-3) }{ 2 } \]

When the number of vertices increases, a beautiful geometric pattern appears.