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Find the polygon… Click on the polygon.

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

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Polygons only have straight sides. They cant have curves. Sorry…

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

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Find the polygon…

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Sorry… Polygons only have straight sides.

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Sorry… Polygons only have straight sides.

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Excellent! All rectangles are polygons.

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Find the polygon…

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

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Sorry… Polygons sides do not cross each other

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All right!

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(1-6) Angles of Polygons The word polygon is a Greek word. Poly gon 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? 1.hexagon 2.octagon 3.pentagon a

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How about this one? 1.octagon 2.hexagon 3.pentagon a

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What is the name of this polygon?... 1.Quadrilateral 2.Pentagon 3.Triangle a

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A polygon with six sides is called a hexagon. 1.True 2.False

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A polygon with 5 vertices is called a quadrilateral. 1.True 2.False a

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An octagon always has 8 equal sides. 1.True 2.False a

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Congratulations!

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A polygon with no side points inwards when extended Convex Polygons 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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180 o 6 sides 180 o 4 x 180 o = 720 o o Interior angles of Polygons 4 sides 2 x 180 o = 360 o 2 5 sides 3 x 180 o = 540 o 3 7 sides 5 x 180 o = 900 o 5

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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 =180 o 1 Exterior angles of Polygons 2

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120 0

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360 0

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60 0

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90 0

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

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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 = Step 2: measure of each ext. angle =

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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 =

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

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

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Homework (12 – 30) even pages 407, 408

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