Polygons

1
Lesson 3-4

• Polygons

2
Polygons
Definition
A closed figure formed by a finite number of
coplanar segments so that each segment intersects
exactly two others, but only at their endpoints.
These figures are not polygons
These figures are polygons
3
Classifications of a Polygon
Convex
No line containing a side of the polygon contains
a point in its interior
Concave
A polygon for which there is a line containing a
side of the polygon and a point in the interior
of the polygon.
4
Classifications of a Polygon
Regular
A convex polygon in which all interior angles
have the same measure and all sides are the same
length
Irregular
Two sides (or two interior angles) are not
congruent.
5
Polygon Names
Triangle
3 sides
4 sides
Quadrilateral
5 sides
Pentagon
6 sides
Hexagon
7 sides
Heptagon
8 sides
Octagon
Nonagon
9 sides
10 sides
Decagon
Dodecagon
12 sides
n sides
n-gon
6
Convex Polygon Formulas..
Diagonals of a Polygon
A segment connecting nonconsecutive vertices of a
polygon
For a convex polygon with n sides
The sum of the interior angles is
The measure of one interior angle is
The sum of the exterior angles is
The measure of one exterior angle is
7
Examples..

• Sum of the measures of the interior angles of a
  11-gon is
• (n 2)180 ? (11 2)180 ? 1620
• The measure of an exterior angle of a regular
  octagon is
• The number of sides of regular polygon with
  exterior angle 72 is
• The measure of an interior angle of a regular
  polygon with 30 sides