## Polygons

The combination of line segments passing through successive ones of three or more points in the plane, of which any three are nonlinear, is called a polygon. These line segments do not intersect except their end points. It is a closed shape that consists of line segments with intersecting all end points.

These extreme points are called the vertices of the polygon, and the line segments connecting consecutive vertices are called the sides of the polygon.

If the extension of any side of the polygon does not intersect the other side, it is called convex polygon, and polygons that cut the other side are called concave (concave) polygons.

The angles between two consecutive sides in a polygon and in the inner region of the polygon are called interior angles of the polygon, and each angle that completes the interior angles or exterior angles of the polygon.

The line segments that join the vertices other than consecutive vertices in a polygon are called the diagonal of the polygon.

### Properties of convex polygons

where n is the number of sides of the polygon;

- The sum of the angles of the polygons is (n-2) .180 °.
- The sum of the dimensions of the outer angles of the polygon is 360 °.
- At least n-3 interior angles of polygons other than square and rectangular are obtuse angles.
- The number of diagonals passing through one corner of the polygon is n-3.
- The number of diagonals is n. (n-3) / 2, with n = 3 and greater than 3.

**Regular Polygons**

A convex polygon with all sides and all angles equal is called a regular polygon.

- An interior angle of a regular polygon; (n-2) .180 / n or 180-360 / n degrees.
- An external angle of a regular polygon; It is 360 / n degrees.
- The perimeter of a regular polygon is equal to the number of sides times one of its sides. S = n.a (a: one side of the regular polygon)
- Area of a regular polygon; The number of sides is equal to half the product of one side and the radius of the inner tangent circle. (We know that the area formula available for all polygons is S = u.r. From here, S = ç / 2.r = n.a.r / 2)
- The center of the inscribed circle and the inner tangent circle of a regular polygon are the same.
- The measure of the arc that one side of a regular polygon separates from its circumferential circle is equal to an outer angle of the regular polygon.
- In a regular polygon, the measure of the arc between two consecutive tangents of the inner tangent circle is equal to an outer angle of the regular polygon.