# 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.

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 – 2

*p*, 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.