Download Polygon

Teacher Notes
Polygons
Objective: To identify and name polygons; to find the sum of the measures of
interior and exterior angles of convex and regular polygons; to solve problems
involving angle measures of polygons.
Terms of Importance
Polygon – A closed figure formed by a finite number of coplanar segments such
that the sides that have a common endpoint are noncollinear and each side
intersects exactly two other sides, but only at their endpoints.
Convex Polygon – A polygon such that no line containing a side of the polygon
contains a point in the interior of the polygon. Examples of convex polygons are
Concave Polygon – A polygon such that lines containing a side of the polygon
that contains a point in the interior of the polygon. Examples of concave
polygons are
n-gon – A polygon with n sides.
Number of Sides
3
4
5
6
7
8
9
10
11
12
N
Polygon
Triangle
Quadrilateral
Pentagon
Hexagon
Heptagon
Octagon
Nonagon
Decagon
Hendecagon
Dodecagon
n-gon
For other names of polygons go to …
http://www.gomath.com/htdocs/ToGoSheet/Geometry/polygon_name.html
Regular Polygon – A convex polygon with all sides and all angles congruent.
Theorems
Interior Angle Sum Theorem – If a convex polygon has n sides and S is the
sum of the measures of its interior angles, then S = 180(n – 2).
Examples
Find the sum of a convex polygon that has 3 sides.
S = 180(3 – 2)
S = 180
Find the measure of each interior angle of a regular hexagon.
First find the sum of all of the angles in a hexagon
S = 180(6 – 2)
S = 720
To find the measure of each interior angle, divide the sum of the angles by the
number of angles in the hexagon
720/6 or 120
Exterior Angle Sum Theorem – If a polygon is convex, then the sum of the
measures of the exterior angles, one at each vertex, is 360.
Example
Use the Exterior Angle Sum Theorem to find the measure of an interior angle
and an exterior angle of a regular pentagon.
A regular pentagon has 5 congruent interior angles. So the measure of each
exterior angle is
360/5 or 72
Because each exterior angle is supplementary to each interior angle, the
measure of each interior angle is
180 – 72 or 108