Download Polygons - C on T ech Math : : An application

Tutorial 5a
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1.
Polygon -- A union of segments
that meet only at endpoints.
Designed by Dave Meyer. All rights reserved
2.
The following are not Polygons. . .
a)
b)A
because a polygon consists
entirely of segments.
D
because in a polygon only
Econsecutive sides intersect
and only at endpoints
F
B
C
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2.
cont...
The following are not Polygons. . .
R
c) P
S
d)
L
because each vertex must
belong to exactly 2 sides
(vertex P belongs to 3).
O
N
D
because each segment
must meet exactly two
other segments.
T
Q
Designed by Dave Meyer. All rights reserved
3.
Parts of Polygons
F
E
•
•
A
D
B
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C
polygon ABCDEF
Vertices:
A, B, C, D, E, F
3.
Parts of Polygons
F
E
•
•
A
D
B
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C
•
polygon ABCDEF
Vertices:
A, B, C, D, E, F
Sides:
AB, BC, CD . . .
3.
Parts of Polygons
F
E
•
•
A
D
B
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C
•
polygon ABCDEF
Vertices:
A, B, C, D, E, F
Sides:
AB, BC, CD . . .
3.
Parts of Polygons
F
E
•
•
A
D
B
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C
•
polygon ABCDEF
Vertices:
A, B, C, D, E, F
Sides:
AB, BC, CD . . .
3.
Parts of Polygons
F
E
•
•
A
D
B
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C
•
polygon ABCDEF
Vertices:
A, B, C, D, E, F
Sides:
AB, BC, CD . . .
3.
Parts of Polygons
F
E
•
•
A
D
B
•
polygon ABCDEF
Vertices:
A, B, C, D, E, F
Sides:
AB, BC, CD . . .
C
Diagonal -- A segment joining 2 nonadjacent
vertices.
Designed by Dave Meyer. All rights reserved
3.
Parts of Polygons
F
E
•
•
A
D
B
Designed by Dave Meyer. All rights reserved
C
polygon ABCDEF
Vertices:
A, B, C, D, E, F
•
Sides:
AB, BC, CD . . .
•
Diagonals
AC, BE, CF . . .
3.
Parts of Polygons
F
E
•
•
A
D
B
Designed by Dave Meyer. All rights reserved
C
polygon ABCDEF
Vertices:
A, B, C, D, E, F
•
Sides:
AB, BC, CD . . .
•
Diagonals
AC, BE, CF . . .
3.
Parts of Polygons
F
E
•
•
A
D
B
Designed by Dave Meyer. All rights reserved
C
polygon ABCDEF
Vertices:
A, B, C, D, E, F
•
Sides:
AB, BC, CD . . .
•
Diagonals
AC, BE, CF . . .
4. Types of Polygons
A polygon is convex if no
diagonal contains points
outside the polygon.
D
A polygon is concave if a
diagonal contains points
outside the polygon.
D
Y
F
H
A
M
T
E
Q
N
4.
cont...
Convex polygon -- A polygon where all
of its diagonals fall on the inside of the
figure.
Which polygon is convex?
Click on your choice.
E
T
V
C
A
U
D
B
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S
Q
R
4.
cont...
Regular Polygon -- A convex polygon
with all of its sides congruent and all
angles congruent.
U
T
V
S
Q
Designed by Dave Meyer. All rights reserved
R
5.
Names of Polygons
Number of sides
3
4
5
6
7
8
9
10
12
20
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Name
triangle
quadrilateral
pentagon
hexagon
heptagon
octagon
nonagon
decagon
dodecagon
icosagon
6.
Finding the sum of the angles of a polygon
The sum of the measures of the interior angles of
a polygon is (n - 2)180. Where n represents the
number of sides.
(n - 2)180
(5 - 2)180 =
(3)180 = 540
The sum of all 5 angles in this polygon is 540º
Designed by Dave Meyer. All rights reserved
6.
cont...
Applications
(n - 2)180
Find the sum of the interior angles of a:
pentagon
decagon
quadrilateral
Click the button below to check your answers!
Designed by Dave Meyer. All rights reserved
6.
cont...
Applications
(n - 2)180
Find the sum of the interior angles of a:
540º
pentagon
decagon
1440º
quadrilateral
360º
Click on the answer to see the problem worked out!
Designed by Dave Meyer. All rights reserved
7. If a polygon has angles with a sum of 720º
then how many sides does the polygon have?
(n - 2)180
180n - 360
180n
n
= 720
= 720
= 1080
= 6
The polygon has 6 sides!
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7.
cont...
Applications
(n - 2)180
How many sides does a polygon have if the sum of
the measures of its interior angles is:
720?
1440?
2700?
Designed by Dave Meyer. All rights reserved
(n-2)180 = 720 ; n = 6 sides
(n-2)180 = 1440; n = 10 sides
(n-2)180 = 2700; n = 17 sides
7.
cont...
More Applications
If the sum of the first five interior angles of a
hexagon is 700, find the measure of the sixth
angle.
(n - 2)180
(6 - 2)180 = 720
720 - 700 = 20
The six angle measures 20º
Designed by Dave Meyer. All rights reserved
8.
Regular Polygon: A polygon that is
both equiangular and equilateral
What’s the formula to find the measure of
each angle of a regular polygon?
(n - 2)180
n
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8.
cont...
Applications
Find the measure of each interior angle of
a regular hexagon
120º
(n - 2)180
n
(6 - 2)180
6
= 720
6
= 120º
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8.
cont...
Applications
 Each interior angle of a regular polygon
measures 135. Find the number of sides
that the polygon has.
(n - 2)180
n
= 135
(n - 2)180
= 135n
= 135n
= - 45n
=n
180n - 360
- 360
8
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9.
Exterior Angles
The sum of the exterior angles
of a polygon is 360
3
4
2
Each exterior angle of a
5
1 regular polygon is 360
6
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n
Summary
The sum of the interior angles of a polygon is
(n - 2)180
Each angle of a regular polygon measures
(n - 2)180
n
The sum of exterior angles is 360
Each exterior angle of a regular polygon is
360
n
Designed by Dave Meyer. All rights reserved
Time to move on to the
assignment or the next lesson.
Designed by Dave Meyer. All rights reserved
6.
cont...
Applications
(n - 2)180
Find the sum of the interior angles of a:
pentagon
A pentagon has 5 sides; So(n – 2)180 =
(5 – 2)180 =
(3)180 = 540º
Designed by Dave Meyer. All rights reserved
Back
6.
cont...
Applications
(n - 2)180
Find the sum of the interior angles of a:
decagon
A decagon has 10 sides; So(n – 2)180 =
(10 – 2)180=
(7)180 = 1440º
Designed by Dave Meyer. All rights reserved
Back
6.
cont...
Applications
(n - 2)180
Find the sum of the interior angles of a:
A quadrilateral has 4 sides; Soquadrilateral
(n – 2)180 =
(4 – 2)180 =
(2)180 = 360º
Designed by Dave Meyer. All rights reserved
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