1. Is there anything invariant about circles?

2. Bell Ringer 10.13.10 CDCD Compare the ratio of the circumference to the diameter C = 9.42 D = 3 C = 12.56 D = 4 C = 15.7 D = 5

3. Circumference Distance around a circle C = D CDCD

5. 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.

6. 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. SidesTriangleDegrees 3 4 5 6 7 8 In Column C, multiply the number of triangles by 180.

7. 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.

8. SidesTriangleDegrees 31180 42360 53540 64720 75900 861080

9. 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

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

11. 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?

13. 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.

14. 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.