Download Regular Polygons Lab Vasile

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?
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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.