Download Slide 1 - Petal School District

Advanced Geometry
Polygons
Lesson 1
Polygons
Polygon
a closed figure
all sides are segments
Examples
NO HOLES
NO CURVES
SIDES
CANNOT
OVERLAP
Diagonal
connects any two nonconsecutive vertices
All diagonals
Diagonals from one
vertex
Convex
Polygon
triangle
quadrilateral
pentagon
octagon
n-gon
# of
Sides
3
4
5
8
n
# of
Triangles
1
2
3
6
n-2
Formula for the
Sum of the Measures
of the Interior Angles
Sum of Interior
Angle Measures
180°
360°
540°
1080°
n-2
180(n - 2)
Example:
Find the sum of the measures of the interior angles
of a convex 23-gon.
Example:
Find the measure of each interior angle.
One Angle of a Regular Polygon
If a polygon is regular,
the measure of each interior angle can be found.
Sum of the
Interior Angles
Number of
Angles
Example:
Find the measure of one interior angle of a
regular nonagon.
Example:
The measure of an interior angle of a regular polygon
is 135. Find the number of sides in the polygon.
Sum of the Measures of the Exterior Angles
If a polygon is convex,
then the sum of the measures of the
exterior angles, one at each vertex is 360.
m1  m2  m3  m4  m5  360
SUM
ONE
Interior
Angles
Exterior
Angles
180  n  2
360
SUM
n
SUM
n
Example:
Find the measures of one interior angle and
one exterior angle of a regular heptagon.
One interior angle and one exterior angle
of a regular polygon will always be supplementary.
Why?
They form a
linear pair.