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T HE P OLYGON
A NGLE -S UM T HEOREM
Geometry Honors
Vocabulary
Polygon –a closed plane figure
formed by three or more segments.
Each segment intersects exactly 2
other segments, but only at their
endpoints, & no two segments
with a common endpoint are
collinear.
Vocabulary
Vertices of a Polygon –the
endpoints of the sides.
Diagonal of a Polygon –a segment
that connects two nonconsecutive
vertices.
Activity
Complete the word search.
Within the word search you will find
the names of various polygons. They
include the names of a:
3 sided polygon, 4 sided polygon,
5 sided polygon, 6 sided polygon, 7
sided polygon, 8 sided polygon, 9
sided polygon, 10 sided polygon, 12
sided polygon and 20 sided polygon.
Types of Polygons
Triangle – a polygon with 3 sides.
Quadrilateral – a polygon with 4
sides.
Pentagon – a polygon with 5 sides.
Hexagon – a polygon with 6 sides.
Types of Polygons
Heptagon – a polygon with 7
sides.
Octagon – a polygon with 8 sides.
Nonagon – a polygon with 9 sides.
Decagon – a polygon with 10
sides.
Types of Polygons
Dodecagon – a polygon with 12
sides.
Icosagon – a polygon with 20
sides.
Discovery
Draw a ______
and then draw as
many diagonals
as you can from
1vertex.
Pentagon
Hexagon
Heptagon
Octagon
Nonagon
n-gon
How many
triangles were
formed?
Determine the
sum of all interior
angles.
Theorem
Polygon Angle-Sum Theorem–the
sum of the measures of the interior
angles of an n-gon is (n-2)*180
Example:
Determine the sum of the interior
angles of an 18 sided figure.
Vocabulary
Equilateral Polygon –a polygon
with all sides congruent.
Equiangular Polygon–a polygon
with all angles congruent.
Regular Polygon –a polygon that is
both equilateral and equiangular.
Vocabulary
Concave Polygon –a polygon that
has at least one diagonal with
points outside the polygon.
Convex Polygon – a polygon with
no diagonal with points outside
the polygon.
Corollary
Corollary to the Polygon Angle
Sum Theorem–the measure of each
interior angle of a regular n-gon is
(n-2)*180
n
Example:
Determine the measure of each
interior angle of a regular octagon.
Application
Example:
Determine the measure of the
missing angle:
x
87
120
32
95
Theorem
Polygon Exterior Angle-Sum
Theorem–the sum of the measures
of the exterior angles of a polygon,
one at each vertex, is 360.
Example:
Find the measure of an exterior
angle of a regular hexagon.
H OMEWORK
Pg. 147:
1-25, 32-35, 40-44, 47-49
.