Download Definition of Polygon

Polygons
Sec: 6.1
Sol: G.10
Definition of Polygon
A polygon is a closed figure formed by an finite number of coplanar segments
such that
 the sides that have a common endpoint are non-collinear
 each side intersects exactly two other sides, but only at their
endpoints.
 Symbolic Representation: Is named by the letters of it’s vertices, in
consecutive order.
Polygons
Not Polygons
A convex polygon is a polygon such that no line
containing a side of the polygon contains a
point in the interior of the polygon.
A polygon that is not convex is called concave.
Concave
Convex
Polygons may be classified by the number of
sides they have. In general, a polygon with n
sides is called an n-gon. This means the
nonagon can also be called a 9-gon. Polygon
Number of Sides
Polygon
3
triangle
4
5
6
7
8
9
10
12
n
Perimeter
Is the sum of the lengths of its sides.
Perimeter of Special shapes:
Triangle
Square
Rectangle
p  abc
p  ssss
p  4s
p  w wl l
p  2 w  2l
Find the Perimeter
Find the Perimeter using the
coordinate plane:
P(-5, 1), Q(-1, 4), R(-6, -8)
Step 1: Graph the points.
Step 2: Use distance formula on all sides.
Step 3: Add the three sides.
Regular polygon
a convex polygon with all angles and all sides
congruent.
Diagonal of a polygon
a segment drawn from one vertex of a polygon
to a nonconsecutive vertex.
Quadrilateral
_________________
_________________
_________________
Notice in each case before this the polygon is separated into
triangles. The sum of the measures of the angles of each
polygon can be found by adding the measures of the angles of
the triangles. This is easy to find since the sum of the angles
in a triangle = ______.
Use the chart below to find a pattern:
Convex
Polygon
triangle
# of sides
quadrilateral
pentagon
hexagon
heptagon
octagon
n-gon
Sum of  measures
3
# of
triangles
1
4
2
2(180) = 360
1(180) = 180
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).
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.
Consider the following regular polygons.
Find the sum of the exterior angles
Find the sum of the measures of the interior angles
of each convex polygon:
1. decagon
2. 21-gon
3. 13-gon
4. 46-gon
The measure of an exterior angle of a regular
polygon is given. Find the number of sides of the
polygon.
5. 30
6. 8
7. 72
8. 14.4
The number of sides of a regular polygon is given. Find
the measures of an interior angle and an exterior
angle for each polygon. Round to the nearest
hundredth
9. 30
10. 9
11. 22
12. 14
The measure of an interior angle of a regular polygon is
given. Find the number of sides in each polygon.
13. 135
14. 144
15. 176.4
16. 165.6
Find the measure of each interior
angle
Suggested Assignments
Classwork: WB pg147-148 2-56 even
Homework: Pg 356-357 7-25, 29, 30, 32, 33