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Warm Up
Draw the figure in the coordinate
plane. Find the perimeter.
A (-1, -2)
B(5, -2)
Lesson 3-4: Polygons
C(5,6)
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Lesson 3-4
Polygons
Lesson 3-4: Polygons
2
Polygons
Definition: A closed figure formed by a finite number of coplanar
segments so that each segment intersects exactly two
others, but only at their endpoints.
These figures are not polygons
These figures are polygons
Lesson 3-4: Polygons
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Are they polygons?
Lesson 3-4: Polygons
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Classifications of a Polygon
Convex: No line containing a side of the polygon contains a point
in its interior
Concave:
A polygon for which there is a line
containing a side of the polygon and
a point in the interior of the polygon.
Lesson 3-4: Polygons
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Classifications of a Polygon
Regular: A convex polygon in which all interior angles have the
same measure and all sides are the same length
The sum of the angles of a polygon with n sides, where n
is 3 or more, is 180 x (n-2) degrees
Irregular:
Two sides (or two interior angles) are not congruent.
Lesson 3-4: Polygons
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Polygon Names
3 sides
Triangle
4 sides
Quadrilateral
5 sides
Pentagon
6 sides
Hexagon
7 sides
Heptagon
8 sides
Octagon
9 sides
Nonagon
10 sides
Decagon
12 sides
n sides
Dodecagon
n-gon
Lesson 3-4: Polygons
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Classifying Triangles by Sides
Scalene: A triangle in which all 3 sides are different lengths.
A
A
B
C
B
BC = 3.55 cm
C
BC = 5.16 cm
Isosceles: A triangle in which at least 2 sides are equal.
G
Equilateral: A triangle in which all 3 sides are equal.
GH = 3.70 cm
H
Lesson 3-1: Triangle
Fundamentals
HI = 3.70 cm
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I
Classifying Triangles by Angles
Acute: A triangle in which all 3 angles are less than 90˚.
G
76
57
47
H
Obtuse:
I
A
A triangle in which one and only one
angle is greater than 90˚& less than 180˚
44
28 108 C
B
Lesson 3-1: Triangle
Fundamentals
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Classification by Sides
with Flow Charts & Venn Diagrams
polygons
Polygon
triangles
Triangle
scalene
Scalene
Isosceles
isosceles
equilateral
Equilateral
Lesson 3-1: Triangle
Fundamentals
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Convex Polygon Formulas…..
Diagonals of a Polygon: A segment connecting nonconsecutive
vertices of a polygon
For a convex polygon with n sides:
The sum of the interior angles is
 n  2 180
The measure of one interior angle is
 n  2  180
n
The sum of the exterior angles is 360
The measure of one exterior angle is
360
n
Lesson 3-4: Polygons
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Examples…..
1. Sum of the measures of the interior angles of a 11-gon is
(n – 2)180°  (11 – 2)180 °  1620
2. The measure of an exterior angle of a regular octagon is
360 360

 45
n
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3. The number of sides of regular polygon with exterior angle 72 ° is
n
360
360
n
5
exterior angle
72
4. The measure of an interior angle of a regular polygon with 30 sides
 n2  180  (302) 180  28 180  168
n
30
Lesson 3-4: Polygons
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Classwork
Identify each polygon by its
sides. Then determine whether it
appears to be regular or not. If
not regular, explain why.
Lesson 3-4: Polygons
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