Find the polygon… Click on the polygon.

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

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

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

Find the polygon…

Polygons only have straight sides. Sorry… Polygons only have straight sides.

Polygons only have straight sides. Sorry… Polygons only have straight sides.

All rectangles are polygons. Excellent! All rectangles are polygons.

Find the polygon…

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

Polygons’ sides do not cross each other Sorry… Polygons’ sides do not cross each other

All right!

(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.

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? hexagon octagon pentagon a

How about this one? a octagon hexagon pentagon

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

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

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

An octagon always has 8 equal sides. True False a

Congratulations!

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)

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.

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

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

1200 600 1200 600 600 1200

1200 1200 1200

1200

3600

600 600 600 600 600 600

600 600 600 600 600 600

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

1 2 3 4 5 6 600

3 4 2 3600 5 1 6

900 900 900 900

900 900 900 900

900

3 2 3600 4 1

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

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 =

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 =

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 =

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 =

Homework (12 – 30) even pages 407, 408