
A polygon is a closed lane figure with at
least three sides that are segments. The
sides intersect only at their endpoints,
and no adjacent sides are collinear.
A
E
B
B
B
A
POLYGON
C
E
A
NOT A
POLYGON
C
C
D
D
NOT A CLOSED FIGURE
D
E
SIDES INTERSECT
Polygons have vertices, sides, and angles
 Vertices: a point where two segments
meet
 Each vertex is also an angle
 Sides are in between two vertices.
 To name a polygon, start at any vertex
and list the vertices consecutively in a
clockwise or counter clockwise direction.



Name the polygon, then identify its
vertices, sides, and angles.
D
Vertices:
H
K
B

Sides:
G

Angles:
M
You can classify
polygons by the
number of sides it
has.


Polygons can also be classified as
convex or concave.
A
M
R
D
CONVEX
T
W
Y
All the vertices of the
polygon will point
outward, away from the
inside of the polygon
CONCAVE
K
G
P
Q
S
A vertex that is pushed
in towards the inside of
the polygon. The
polygon “caves” in.

Classify each polygon by the number of
sides and identify if it is concave or
convex.

3-9 Polygon Angle-Sum Theorem
› The sum of the measures of the interior
angles of an n-gon is 𝑛 − 2 180
Polygon
Number of Sides
Number of
Triangles Formed
Sum of the
Interior Angles

Find the measure of the angles of a
15-gon.

Find m∠y.
R
T
Y
V
M

3-10 Polygon Exterior Angle-Sum
Theorem
› The sum of the measures of the exterior
angles of a polygon, one at each vertex, is
360°
3
› For the pentagon
2
m∠1 + m∠2 + m∠3 +m∠4 + m∠5 = 360°
4
1
5
An equilateral polygon has all sides
congruent.
 An equiangular polygon has all angles
congruent.
 A regular polygon is both equilateral and
equiangular.


Find the measure of each given the
figure is a regular polygon.
a.
Sum of the interior angles
b.
The measure of 1 interior angle
c.
The sum of the exterior angles
d.
The measure of 1 exterior angle

The sum of the measure of the angles of
a polygon is 4,500. Find how many sides
the figure has.

The measure of an exterior angle of a
regular polygon is 40°. Find the measure
of an interior angle, and the number of
sides.
Pg 147-148
 1-25, 32-35
