Is there anything invariant

about circles?

Bell Ringer 10.13.10

CD

Compare the ratio of the circumference to the diameter

C = 9.42D = 3

C = 12.56D = 4

C = 15.7D = 5

CircumferenceDistance around a circle

C = • D

CD

In this activity you will use triangles and the Triangle Angle-Sum Theorem to find the sum of the measures of the angles of a polygon. You will construct polygons with 4, 5, 6, 7, and 8 sides. Then you will use line segments to divide the polygon into triangles using the same vertex for each line segment. The data will be recorded into a table for analyzing. Please follow the directions on the following pages.

1) Construct a 4 sided figure

1) Divide the figure into triangles using line segments that start from the same vertex.

1) Record your data in the table.

Sides Triangle Degrees

345678

In Column C, multiply the number of triangles by 180.

1)Construct a 5-sided figure.

Divide the figure into triangle using line segments which start from the same vertex.

Record data in the table.

2) Construct a 6-sided figure.Divide the figure into triangle using line segments which start from the same vertex.Record data in the table.

3) Construct a 7-sided figure.Divide the figure into triangle using line segments which start from the same vertex.Record data in the table

4) Construct a 8-sided figure.Divide the figure into triangle using line segments which start from the same vertex.Record data in the table.

Sides Triangle Degrees

3 1 180

4 2 360

5 3 540

6 4 720

7 5 900

8 6 1080

Analyze the data and look for a pattern. Write a formula that relates to your data.

The degrees of a n-sided polygon

= (n-2)180

Example

Using your new formula, what is the sum of the measure of the angles in a 10-sided polygon?

Homework Pg. 57 #12 (next slide) What is the sum of the measures of the angles of a 20-sided

polygon? 9-sided polygon? 17-sided polygon? What is the area of the

shaded region?

Bell Ringer October 13, 2010

Tennis balls are sold in cans of three. Which is greater, the height of the can or the circumference of the can?

Quick Write – 2 minutes to explain your answer

Go to the front of the room if you think the height of the can is greater.

Go to the back of the room if you think the circumference is greater.

Solution

We know the height of the can is 6r.Circumference equals 2 πr.

2 (3.14)r = 6.28r

6.28r > 6r So, the circumference of the can is greater than the height of the can.