## Diagonal of a polygon

### The diagonal of a polygon is a line segment that connects two non-adjacent vertices of the polygon

The diagonal of a polygon is a line segment that connects two non-adjacent vertices of the polygon. In other words, it is a line segment that goes from one corner of the polygon to another corner that is not next to it.

To visualize this, imagine a triangle. The diagonal of a triangle would connect two vertices that are not adjacent, for example, the line segment connecting the top vertex to the bottom left or bottom right vertex. Similarly, in a quadrilateral or a pentagon, the diagonal would connect two vertices that are not neighboring each other.

It is important to note that not all polygons have diagonals. Diagonals are only present in polygons with three or more sides. Furthermore, the number of diagonals in a polygon depends on the number of sides it has.

The length of a diagonal can be calculated using the distance formula from analytic geometry, which is derived from the Pythagorean theorem. However, in some cases, the length of the diagonal may be given or can be found using other geometric properties of the polygon.

The presence of diagonals in a polygon can have various applications in geometry and can be used to determine properties such as the number of triangles formed by diagonals, the total number of diagonals, and even the interior angles of the polygon.

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