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