Chapter 3 Lesson 4

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Chapter 3 Lesson 4

• Objective To classify polygons.

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Polygon a closed plane figure with at least
three sides that are segments. The sides
intersect only at their endpoints, and no
adjacent sides are collinear.
B
B
B
A
A
A
C
C
C
D
D
E
E
D
E
Not a polygon two sides intersect between
endpoints
Not a polygon not a closed figure
A polygon
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Example 1Naming a Polygon
Name the polygon. Then identify its vertices,
sides, and angles.
To name a polygon, start at any vertex and list
the vertices consecutively in a clockwise or
counterclockwise direction.
Two names for this polygon are ABCDE and CDEAB.
Vertices A,B,C,D,E
Sides AB, BC, CD, DE, EA
Angles A, B, C, D, E
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Example 2Naming a Polygon
Three polygons are pictured. Name each polygon,
its sides and its angles.
B
C
A
D
E
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You classify a polygon by the number of sides it
has.
Sides Name
3 Triangle
4 Quadrilateral
5 Pentagon
6 Hexagon
8 Octagon
9 Nonagon
10 Decagon
12 Dodecagon
n n-gon
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Convex polygon has no diagonals with points
outside the polygon.
A
B
C
E
Diagonals
D
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Concave polygon has at least one diagonal with
points outside the polygon.
C
D
B
E
F
A
G
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Example 3
Classify each polygon by its sides. Identify each
as convex or concave.
a.
b.
Hexagon Convex
Octagon Concave
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Theorem 3-9 Polygon Angle-Sum Theorem The sum of
the measures of the angles of n-gon is (n-2)180.
Example 4
Find the sum of the measures of the angles of a
15-gon.
For a 15-gon, n 15
Sum (n 2)180 (15 2)180 13180 2340
Polygon Angle-Sum Theorem Substitute Simplify
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Example 5Finding a Polygon Angle Sum
Find the sum of the measures of the angles of a
decagon.
Decagon 10 (n-2)180 (10-2)180 8180 1440
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Theorem 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.
For the pentagon, m 1 m 2 m 3 m
4 m 5 360.
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Example 6Finding Exterior Angles of a Polygon
80150x360 230x360 x130
80
150
x
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Equilateral Polygon all sides congruent.
Equiangular Polygon all angles congruent.
Regulae Polygon is both equilateral and
equiangular.
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Homework
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