Download Chapter 6 Polygons and Quadrilaterals

Standard G-4: The student will demonstrate
an understanding of quadrilaterals and
other polygons, their properties, and
relationships between or among them.
 Objectives:
 Introduction to polygons
 To find the sum of the measures of
interior angles of a polygon
 To find the sum of the measures of
exterior angles of a polygon
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Polygon
Convex polygon
Concave polygon
Equilateral polygon
Equiangular polygon
Regular polygon
Interior angles
Exterior angles
A polygon is a closed plane figure with 3 or more sides (all straight lines, no curves).
Which of the following figures are polygons?
Example: Name the 3 polygons
Top
S
XSTU
T
Bottom
X
W
U
V
WVUX
Big
STUVWX
Two Types of Polygons
Convex – all vertices point outward
Concave – at least one vertex points inward towards the
center of the polygon (The side looks like it “caved” in)
Classifying Polygons by # of Sides
3 sided Polygon =
Triangle
Hint: Think “Tri”cycle, “tri”pod,
“Tri”lateration (Tri means 3)
Classifying Polygons by # of Sides
4 sided Polygon =
Quadrilateral
Hint: Think “Quad”rant,
“Quad”ruple, “Quad” (AKA 4Wheeler)
Classifying Polygons by # of Sides
5 sided Polygon =
Pentagon
Hint: Think “Pent”athalon, or the
government building “The Pentagon”
Classifying Polygons by # of Sides
6 sided Polygon =
Hexagon
Hint: Both “Hexagon” and “Six” have
an ‘x’ in them
Classifying Polygons by # of Sides
7 sided Polygon =
Heptagon
Hint: ???
Classifying Polygons by # of Sides
8 sided Polygon =
Octagon
Hint: “oct”opus – 8 legs
Classifying Polygons by # of Sides
9 sided Polygon =
Nonagon
Hint: “Non” is similar to “Nine”
Classifying Polygons by # of Sides
10 sided Polygon =
Decagon
Hint: Think “Dec”ade (10 years)
Classifying Polygons by # of Sides
11 sided Polygon =
Hendecagon
Hint: ???
Classifying Polygons by # of Sides
12 sided Polygon =
Dodecagon
Hint: ???
Classifying Polygons by # of Sides
Q: What do we call a polygon with more than 12 sides?
A: An ‘n’-gon where ‘n’ is the number of sides
Ex: a 20 sided polygon is a 20-gon
Classifying Polygons by # of Sides
# of Sides
Name
3
Triangle
4
Quadrilateral
5
Pentagon
6
Hexagon
7
Heptagon
8
Octagon
9
Nonagon
10
Decagon
11
Hendecagon
12
Dodecagon
Regular Polygons
A Regular Polygon is a polygon in which all sides are the same length.
Equilateral Triangle 
 Square
Polygon Angle-Sum
Theorem 1
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Example:
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 Solve for x in the following example.
x
100
Example:
Find the measure of one interior  of a
regular hexagon.
Polygon Angle-Sum
Theorem 2
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Exterior s of a polygon.
1
3
2
1
2
3
4
5
Example:
How many sides does a regular polygon
have if it has an exterior  measure of 36°.
Example:
Find the sum of the interior s of a regular
polygon if it has one exterior  measure of 24.
Real world connections
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 A company is manufacturing a gear that has the
shape of a regular polygon. The measure of each
angle of the gear is 162. How many sides does the
gear have?
Real world connections
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 The car at each vertex of a Ferris wheel holds a
maximum of 5 people. The sum of the measures of
the angles of the Ferris wheel is 7740. What is the
maximum number of people that the Ferris wheel
can hold?
Practice/Homework
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 Textbook: page #356
 Problems: 1-25 all problems and 29-35
 Show your work.