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 halfperimeter). We consider only simple polygons in an elementary geometry, contours of which have no selfintersections ( 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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