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Find the polygon… Click on the polygon.

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**Polygons are closed shapes. They cannot have openings.**

Sorry… Polygons are closed shapes. They cannot have openings.

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**Polygons only have straight sides. They can’t have curves.**

Sorry… Polygons only have straight sides. They can’t have curves.

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**Polygons are closed shapes All triangles are polygons.**

Congratulations! Polygons are closed shapes with straight sides. All triangles are polygons.

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Find the polygon…

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**Polygons only have straight sides.**

Sorry… Polygons only have straight sides.

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**Polygons only have straight sides.**

Sorry… Polygons only have straight sides.

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**All rectangles are polygons.**

Excellent! All rectangles are polygons.

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Find the polygon…

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**Polygons are closed figures.**

Sorry… Polygons are closed figures. They do not have holes.

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**Polygons’ sides do not cross each other**

Sorry… Polygons’ sides do not cross each other

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All right!

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**(1-6) Angles of Polygons Poly means many and gon means angle.**

The word ‘polygon’ is a Greek word. Poly means many and gon means angle.

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**Definition of polygon A closed object**

Made up of straight line segments that do not cross each other Vertex Side

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**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

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**What is the name of this polygon?**

hexagon octagon pentagon a

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How about this one? a octagon hexagon pentagon

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**What is the name of this polygon?...**

Quadrilateral Pentagon Triangle a

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**A polygon with six sides is called a hexagon.**

True False

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**A polygon with 5 vertices is called a quadrilateral.**

True False a

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**An octagon always has 8 equal sides.**

True False a

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Congratulations!

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**Convex Polygons Concave Polygons**

A polygon with no side points inwards when extended Concave Polygons A polygon with at least one side points inwards when extended. (Think: concave has a "cave" in it)

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**Regular Polygons A polygon is regular when all the angles are equal**

and all of the sides are congruent

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**Diagonals of Polygons Diagonal**

A line segment that connects two non consecutive vertices of a polygon.

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**Interior angles of Polygons**

4 sides 5 sides 2 x 180o = 360o 3 x 180o = 540o 2 3 180o 180o 180o 180o 180o 180o 6 sides 4 x 180o = 720o 7 sides 4 5 x 180o = 900o 5

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**Exterior angles of Polygons**

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 2 1 Exterior Angle + Interior Angle =180o

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1200 600 1200 600 600 1200

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1200 1200 1200

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1200

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3600

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600 600 600 600 600 600

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600 600 600 600 600 600

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1 2 3 4 5 6 600 600 600 600 600 600

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1 2 3 4 5 6 600

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3 4 2 3600 5 1 6

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900 900 900 900

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900 900 900 900

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900

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3 2 3600 4 1

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** Sum of exterior angles = 360º**

Sum of Interior Angles = (n – 2) 180 # of sides Sum of exterior angles = 360º exterior angle + interior angle = 180º Regular polygons Measure of each exterior angle of a regular polygon = # of sides of a regular polygon = # of sides

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**Example1: Find the measure of each interior angle of a regular nonagon**

Step 1: Nonagon has 9 sides so n=9 Step 2: measure of each ext. angle = Step 3: measure of interior angle =

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Example2: Find the measure of each exterior angle of a regular decagon. Step 1: Decagon has 10 sides so n=10 Step 2: measure of each ext. angle =

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Example3: How many sides are there in a regular polygon if each interior angle measures 165o? Step 1: measure of exterior angle = Step 2: # of sides of a regular polygon =

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Example4: Is it possible to have a regular polygon with an exterior angle equal to 40o ? If yes find the number of sides Step 1: yes Step 2: # of sides =

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Homework (12 – 30) even pages 407, 408

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3.6 Angles in Polygons Objectives: Warm-Up:

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