Convex polygon
A polygon is called convex if for any two of its points the segment with the ends at these points completely belongs to the polygon. Or in other words, a polygon is convex if it is entirely located on one side of a line passing through any two adjacent vertices.
Opposite vertices of a polygon are any two vertices that do not lie on the same side of the polygon. A segment connecting any two opposite vertices is called a diagonal of the polygon:
A convex n-gon is a convex polygon with n sides. Thus, a triangle is a polygon with 3 sides, a quadrilateral is a polygon with 4 sides, and so on. Any triangle is a convex figure:
A quadrilateral can be either convex or non-convex:
A regular polygon is a convex polygon in which all sides are equal and all angles are equal.
In the future, we will consider only convex figures.
The points are called the vertices of the broken line, and the segments are called links. When the end of the last segment coincides with the beginning of the first, the broken line is called closed:
A polygon is a part of a plane bounded by a closed broken line, in which no two adjacent segments lie on the same line, and no two non-adjacent segments intersect each other. The vertices and links of the broken line are called the vertices and sides of the polygon, respectively.
The perimeter of a polygon is the sum of the lengths of all sides of the polygon. Half of the perimeter is called the semiperimeter.
