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Find the polygon…Click on the polygon.
Sorry…
Polygons are closed shapes.
They cannot have openings.
Polygons only have straight sides. They can’t have curves.
Sorry…
Congratulations!
Polygons are closed shapes
with straight sides.
All triangles are polygons.
Find the polygon…
Sorry…
Polygons only have straight sides.
Sorry…
Polygons only have straight sides.
Excellent!
All rectangles are polygons.
Find the polygon…
Sorry…
Polygons are closed figures.
They do not have holes.
Sorry…
Polygons’ sides do not cross each other
All right!
(1-6) Angles of Polygons
The word ‘polygon’ is a Greek word.
PolyPoly means many
and gongon means angle.
Definition of polygon• A closed object• Made up of straight line segments• that do not cross each other
Vertex
Side
Names of some polygons
• Triangle• Quadrilateral• Pentagon• Hexagon• Heptagon • Octagon • Nonagon• Decagon• n-gon
• 3-sides• 4-sides• 5-sides• 6-sides• 7-sides• 8-sides• 9-sides• 10-sides• n -sides
What is the name of this polygon?
1. hexagon
2. octagon
3. pentagon
a
How about this one?
1. octagon
2. hexagon
3. pentagon
a
What is the name of this polygon?...
1. Quadrilateral
2. Pentagon
3. Triangle
a
A polygon with six sides is called a hexagon.
1. True
2. False
A polygon with 5 vertices is called a quadrilateral.
1. True
2. False
a
An octagon always has 8 equal sides.
1. True
2. False
a
Congratulations!
A polygon with no side points inwards when extended
Convex Polygons
Concave PolygonsA polygon with at least one side points inwards when extended.
(Think: concave has a "cave" in it)
Regular Polygons
A polygon is regular when
all the angles are equal
and all of the sides are congruent
Diagonals of Polygons
Diagonal
A line segment that connects two non consecutive vertices of a polygon.
180o 180
o
180o
180o
180o
6 sides
180o
180o
180o
180o
4 x 180o = 720o 4
180o
180o180o
180o
180o
Interior angles of Polygons
4 sides2 x 180o =
360o 2 5 sides
3 x 180o = 540o 3
7 sides5 x 180o =
900o 5
An exterior angle of a regular polygon is formed by extending one side of the polygon.
Angle 1 is an exterior angle to angle 2
Exterior Angle + Interior Angle =180o
1
Exterior angles of Polygons
2
1200
1200
1200
600 600
600
1200
1200
1200
1200
1200
1200
3600
600
600
600
600
600
600
600
600
600
600
600
600
1
2
3
4
5
6
600
600600
600
600600
1
2
3
4
5
6
600
600600
600
600 600
1
2
34
5
6
3600
900
900
900
900
900
900
900
900
900
900
900
900
1
23
4
3600
Sum of exterior angles = 360º
Sum of Interior Angles = )n – 2( 180
# of sides
Regular polygonsRegular
polygonsMeasure of each exterior angle of a regular polygon =
# of sides of a regular polygon =
n
360
.360
ext # of sides
exterior angle + interior angle = 180º
Find the measure of each interior angle of a regular nonagon
Example1:
Step 1: Nonagon has 9 sides so n=9
Step 3: measure of interior angle = 14040180
Step 2: measure of each ext. angle = n
360
9
360 40
Find the measure of each exterior angle of a regular decagon.
Example2:
Step 1: Decagon has 10 sides so n=10
Step 2: measure of each ext. angle = n
360
10
360 36
How many sides are there in a regular polygon if each interior angle
measures 165o?
Example3:
Step 2: # of sides of a regular polygon = .
360
ext 15
360 sides24
Step 1: measure of exterior angle = 15165180
Is it possible to have a regular polygon with an exterior angle equal to
40o ? If yes find the number of sides
Example4:
Step 2: # of sides = .
360
ext 40
360 sides9
Step 1: yes
Homework
)12 – 30( even
pages 407, 408