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Polygon

Polygon. Vertices, angles, diagonals, sides of a polygon.
Perimeter of a polygon. Simple polygons. Convex polygon.
Sum of interior angles in a convex polygon.

A plane figure, formed by closed chain of segments, is called a  polygon. Depending on a quantity of angles a polygon can be a triangle, a quadrangle, a pentagon, a hexagon etc. On  Fig.17  the hexagon ABCDEF is shown. Points


A, B, C, D, E, F vertices of polygon; angles  A , B , C , D, E , F angles of polygon; segments AC, AD, BE etc. are diagonals; AB, BC, CD, DE, EF, FA sides of polygon; a sum of sides lengths AB + BC + + FA is called a perimeter of polygon and signed as  p (sometimes 2p, then p a half-perimeter). We consider only  simple polygons in an elementary geometry, contours of which have no self-intersections  ( as shown on Fig.18 ). If all diagonals lie inside of a polygon, it is called a convex polygon. A hexagon on  Fig.17 is a convex one;  a pentagon ABCDE on  Fig.19 is not a convex polygon, because its diagonal AD lies outside of it. A sum of interior angles in any convex polygon is equal to 180 ( n 2 ) deg, where  n  is a number of angles (or sides) of a polygon.

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