In Part C, we explore the interior and exterior angles of a figure as well as the relationship between the two. For the problems in this section, you will engage in an Interactive Activity based on computer software called Geo-Logo. Note 6 You will enter commands that cause the cursor to draw shapes and designs on the screen. Your commands make the cursor draw line segments a given distance forward or backward, or turn the cursor a given number of degrees to the right or the left. This activity will provide you with a different method of exploring angle measurement.
When you've completed each shape, print the page so that you have a record of your shapes and of the commands you entered to draw them.
Problem C2
a.
What is the relationship between the amount of a turn and the resulting interior angle? For example, when you Rotate Right 30, the amount of turn is 30 degrees. What is the resulting angle measure?
b.
Why is this relationship important to understand?
Problem C3
Examine the polygons you drew where your turns were all in one direction (either all to the right or all to the left). What is the sum of the measures of the exterior angles of each of these polygons? Is this sum the same for all polygons? Why or why not? Note 7
Problem C4
Use your drawings to determine the relationship between the measure of central angles and the measure of exterior angles in regular polygons. Explain this relationship.
Try this with simpler shapes, such as an equilateral triangle. Close Tip
Video Segment Watch this segment to see Mary and Susan experiment with Geo-Logo commands to create different regular polygons. They examine the relationship between the angle of turn and exterior and interior angles.
Do you think computer technology can enhance exploring mathematical tasks such as this one? Why or why not?
If you are using a VCR, you can find this segment on the session video approximately 16 minutes and 47 seconds after the Annenberg Media logo.
In order to draw a non-intersecting star polygon, you must direct the cursor to turn both right and left. Print a copy of the star polygons and measure the exterior angles. What is the sum of the exterior angles in a star polygon? Explain this result using the commands.
Think about how turning in both directions affects the resulting exterior angles. Close Tip
