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Polygons

A Polygon is a closed plane figure formed by 3 or more segments

Each segment intersects exactly 2 other segments only at their endpoints.

No 2 segments with a common endpoint are collinear

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Sides

• The segments that form a polygon are called its sides.

• In a polygon, no 2 segments with a common endpoint are collinear

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Vertex of a Polygon

• The vertex of a polygon is the intersection of 2 of its sides.

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EQUIANGULAR POLYGON

• An equiangular polygon is a polygon in which all angles are congruent

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Equilateral Polygon

• An equilateral polygon is a polygon in which all sides are congruent.

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REGULAR POLYGON

• If a polygon is both equiangular and equilateral, then it is called regular.

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Irregular Polygon

• If a polygon is not equiangular and equilateral, then it is an irregular polygon

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Polygons named by number of sides

11 sided polygon - hendecagon

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Diagonal of a polygon

• A diagonal of a polygon is a segment that connects 2 nonconsecutive vertices.

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Convex polygon• In a convex polygon, every diagonal lies inside

it

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Concave polygon• In a concave polygon, at least 1 diagonal can be

drawn so that part of it contains points in the exterior of the polygon

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Congruent polygons• If 2 polygons have the same size and

shape, they are congruent

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Interior and Exterior angles of polygons• At each vertex, there are 2 special angles.

• An interior angle is an angle fprmed by 2 sides of a polygon with a common vertex

• An exterior angles is an angle formed by 1 side of a polygon and the extension of an adjacent side

E

I

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Formula for sum of interior angles of a polygon

• n is the number of sides

sum of interior angles = (n-2) 180o

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Formula for interior angles measure of a regular polygon

• n is the number of sides

• Each interior angle =

n

n

2 180b g

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Formula for exterior angle measure of a regular polygon

• n is the number of sides

360

n

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Center of a regular polygon• Center is the point that is

equidistant from each of the polygon's vertices

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Central angle of a regular polygon

• Central angle has its vertex at the center of the polygon and its sides pass through consecutive vertices

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Formula for central angle measure of a regular polygon

• n is the number of sides

360

n

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