The ins and outs of polygons

Interior angle: The angle inside a polygon formed by 2 adjacent sides of a polygon. (the angles inside the figure)
-Jacks ideas: (# of sides-2) x 180= sum of anterior angles 
-Delany's: (# of sides x 180) -(180x2)= sum of anterior angles 

Exterior angle: Are measured by extending a side of a convex polygon and measuring the angles that lie outside the line. 

-The sum of all exterior angle measures is 360. 

*What is the relationship between interior and exterior angles? 
-They are supplementary: If you add them together they equal 180. 


Label the exterior angles and the interior angles. 

Predict: 
What would be the sum of all the angles? 

Track problem: 
What is the sum total of those left turns? No math, make a reasoning as to what it is going to be. 

As there are more sides, the shapes become more circular.

Tiling

Tiling

You can use 2 shapes, but you can't have any overlap or gap.

Think about what you know for tessellations:

The shapes that tessellate make 360 degrees. The shapes that do not make more than 360 degrees.

Tesselate

We watched this video in class.


http://www.youtube.com/watch?v=X9lJhDLtFeM




The hexagons in a beehive all tessellate. What do we think the definition of tessellation is?

Which of these regular polygons can tessellate and which can not?

Why do certain polygons tessellate? Make 5 observations.

What do you notice this student did?

The shapes that tessellate make 360 degrees (or are factors). The shapes that do not make more than 360 degrees.

Irregular Polygon Observations and Rules

In your group, choose three strong observations. Then, make a rule that can be used for all irregular polygons to find the sum of all the angles.(Devon, Casey, Trevor ideas)

Devon

-angle measure=180

-quad measure=360

-added 180 each time

1. (# sides x 180)- 360   Guess and Check!

2. (# of sides -2) x 180   When you change some get smaller and bigger--total same. 

Trevor 

Casey

 

Finidng the Sum of all angle measures.

The Sum of all angle measures for polygons

Jack's: ( # of sides-2) x180= sum of angle measure



Delany's: (# of sides x 180) -(180 x 2) 



360/4= 90 (square) 
1440/10=144 (Decagon)

To find the single angle measure
Sum of the angle measures 

sum of the angle measures/# of sides= single angle measure 
 
1. Devon: Tore off the corners and put them together. 

2. Trevor:Tried to cut them up into equal pieces. Used the lines to create certain degrees and added them together. Maybe tried to cut the shapes into triangles to find the sum of the angles.

 3. Casey: Put a dot near the center of the shape and made them into triangles. Number of sides of the shape was the same as the #of triangles.

*Make as many observations as you can. Is there a relationship between the number of sides in the polygons and the angle measure?