The main idea of this problem is to look for patterns in finding the sum of all of the "interior angles" for a regular polygon with any number of sides. Using the pattern, we should then be able to create a formula for finding the sum of the angles for any polygon as well as a formula for finding the size of any one angle in a regular polygon.
In this lesson, we will explore the following "regular polygons":
Using a protractor, carefully measure one of the angles for shapes A, B, C, and D and record them in the table below. See if you can then determine the "Angle Sum" for the four polygons.
- See if you can find any patterns in your table. If so, try to extend those patterns in order to fill out the rest of the table.
- Answer Questions 1-4 for Task A
- Discuss Task B in your group.
- The most difficult part of this lesson is trying to write a rule (formula) that would allow you to determine the "Angle Sum" based on the number of sides for any polygon (Task C) as well as the size of each angle in a regular polygon if you know the number of sides (Task D)
At the end of this problem you should be able to do the following:
- Calculate the "Angle Sum" for any polygon if you know the number of sides.
- Determine the "Measure of an Angle" for any regular polygon if you know the number of sides.
- Describe the difference between "regular" and "irregular" polygons.
HOMEWORK:
- 2.1 ACE Problems (1, 2) (17, 18) (22)
- Make a Blog Post to address the "Investigation 1 Reflection Questions" (pg. 39). Be sure to label your blog post so that I can find it. Check out the rubric here.
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