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Transcript
Regular Polygons Project Geometry, Ms. Vasile Name: 1. Complete the table showing the relationship between the number of sides in the regular polygon and the measures of its central angle. #sides:__________________________________________________ central angle 2. What happens to the measure of the central angle as the number of sides increases? 3. How low do you think the measure of the central angle can go? (for example, if you have 100 sides or 1,000 sides or 1,000,000 sides) 4. Can you write a formula where n is the number of sides in order to calculate the measure of the central angle? ******************************************************************* 5. Complete the table showing the relationship between the number of sides in the regular polygon and the measures of its interior angles. # sides: _________________________________________________ interior angle 6. What happens to the measure of the interior angle as the number of sides increases? 7. What is the sum of the central angle + the interior angle for regular polygons of 3 sides? 4 sides? 5 sides? 6 sides? 7 sides? 8 sides? What do you notice? Why is this? 8. Can you write a formula where n equals the number of sides to describe the measure of an interior angle? 9. What do you think the maximum value of the measure of the interior angle will be? Why? 10. Complete the following tables about the sums of a regular polygon’s central angles and the sums of a regular polygon’s interior angles. Write a paragraph about what you notice. #sides:__________________________________________________ sum of central angles #sides:__________________________________________________ sum of interior angles Observation of Isosceles Triangles: Examine isosceles triangles you have created in each regular polygon. Record the following information for 4 different regular polygons. # sides: Measure of vertex angle: Measure of base angles: # sides: Measure of vertex angle: Measure of base angles: # sides: Measure of vertex angle: Measure of base angles: # sides: Measure of vertex angle: Measure of base angles: Draw a picture explaining how your observations of isosceles triangles relate to Question #7.