Polygons

1
Lesson 1-6

• Polygons

2
Transparency 1-6
5-Minute Check on Lesson 1-5
A

• Refer to the figure for questions 1 through 3.
• Name two acute vertical angles.
• Name a linear pair whose vertex is E.
• Name an angle supplementary to ?BEC.
• If ?1 and ?2 are supplementary and the measure of
  ?1 is twice that of ?2, then find the measures of
  both angles.
• If RS ? ST and SV is the angle bisector of ?RST,
  what is the m ?TSV?
• If
  two angles are congruent and supplementary, then
  they must be

D
48
E
B
C
Standardized Test Practice
A
two right angles
B
two acute angles
an acute and an obtuse angle
D
two obtuse angles
C
Click the mouse button or press the Space Bar to
display the answers.
3
Transparency 1-6
5-Minute Check on Lesson 1-5
A

• Refer to the figure for questions 1 through 3.
• Name two acute vertical angles.
• Name a linear pair whose vertex is E.
• Name an angle supplementary to ?BEC.
• If ?1 and ?2 are supplementary and the measure of
  ?1 is twice that of ?2, then find the measures of
  both angles.
• If RS ? ST and SV is the angle bisector of ?RST,
  what is the m ?TSV?
• If
  two angles are congruent and supplementary, then
  they must be

D
48
m ?AEB m ?DEC 48
E
B
C
Samples ?AEB and ?AED or ?BEC and ?CED
Either ?AEB or ?DEC
m?1 m?2 180 supplementary
m?1 2m?2 so 2m?2 m?2 180 3m?2 180
m?2 60

m?1 120
m ?TSV ½ m ?RST ½(90) 45
Standardized Test Practice
A
two right angles
B
two acute angles
an acute and an obtuse angle
D
two obtuse angles
C
Click the mouse button or press the Space Bar to
display the answers.
4
Objectives

• Identify and name polygons
• Find perimeters of polygons

5
Vocabulary

• Polygon a closed figure whose sides are all
  line segments
• n-gon a polygon with n sides
• Concave any line aligned to the sides passes
  through the interior
• Convex not concave (side line passes through
  interior)
• Regular polygon a convex polygon with all
  segments congruent all angles congruent
• Irregular polygon not regular
• Perimeter the sum of the lengths of sides of
  the polygon

6
Not a Polygon
Sides are not line segments
Figure is not closed
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Polygons
Side extended goes through interior
Concave
Convex
Not Concave All extended sidesstay outside
interior All Interior Angles less than 180
Interior Angle gt 180
Irregular
Regular
All Sides same All Angles same
Not Regular
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Perimeter
P a b c d e f
e
d
f
Once around the figure
a
c
If regular, then a b c d e fand P 6a
b
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Names of Polygons
Number of Sides Name Sum of Interior Angles
3 Triangle 180
4 Quadrilateral 360
5 Pentagon 540
6 Hexagon 720
7 Heptagon 900
8 Octagon 1080
9 Nonagon 1260
10 Decagon 1440
12 Dodecagon 1800
n N-gon (n-2) 180
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Example 6-1a
Name the polygon by its number of sides. Then
classify it as convex or concave, regular or
irregular.
There are 4 sides, so this is a quadrilateral.
No line containing any of the sides will pass
through the interior of the quadrilateral, so it
is convex.
The sides are not congruent, so it is irregular.
Answer quadrilateral, convex, irregular
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Example 6-1b
Name the polygon by its number of sides. Then
classify it as convex or concave, regular or
irregular.
There are 9 sides, so this is a nonagon.
A line containing some of the sides will pass
through the interior of the nonagon, so it is
concave.
The sides are not congruent, so it is irregular.
Answer nonagon, concave, irregular
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Example 6-2a
CONSTRUCTION A masonry company is contracted
to lay three layers of decorative brick along the
foundation for a new house given the dimensions
below. Find the perimeter of the foundation.
Add the sides lengths
13
Example 6-4a
The width of a rectangle is 5 less than twice its
length. The perimeter is 80 centimeters. Find
the length of each side.
P l w l w 2(l w)
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Example 6-4b
Perimeter formula for rectangle
Multiply.
Simplify.
Add 10 to each side.
Divide each side by 6.
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Summary Homework

• Summary
• A polygon is a closed figure made of line
  segments
• The perimeter of a polygon is the sum of the
  lengths of its sides
• Homework
• pg 49-50 12-21, 29-31, 33