Find the polygon Click on the polygon Sorry

Find the polygon… Click on the polygon.

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

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

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. 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? 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!

Convex A polygon with no side points. Polygons 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 180 o 180 o 4 sides 2 180 o 2 x 180 o = 360 o 180 o 5 sides 3 180 o 3 x 180 o = 540 o 180 o 180 o 6 sides 4 4 x 180 o = 720 o 7 sides 5 5 x 180 o = 900 o

Exterior angles of An exterior angle of a regular. Polygons 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 =180 o

1200 600 1200

1200

1200

3600

600 600 600

600 600 600

3 4 600 2 600 5 600 1 6

3 4 600 2 600 5 600 1 6

3 4 2 3600 5 1 6

900 900

900 900

900 900

2 3 3600 4 1

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

Example 1: 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 =

Example 2: 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 =

Example 3: How many sides are there in a regular polygon if each interior angle measures 165 o? Step 1: measure of exterior angle = Step 2: # of sides of a regular polygon =

Example 4: Is it possible to have a regular polygon with an exterior angle equal to 40 o ? If yes find the number of sides Step 1: yes Step 2: # of sides =

Homework (12 – 30) even pages 407, 408