In Part C, we explore the interior and exterior angles of a figure as well as the relationship between the two. This activity will provide you with a different method of exploring angle measurement.
On a piece of paper draw the following shapes. Pay attention to the amount of turn you do with your pencil as you draw any two adjacent sides (the amount of turn will be equal to the exterior angle of the polygon at that vertex).
a.
Square
b.
Rectangle
c.
Parallelogram that is not a rectangle
d.
Equilateral triangle
e.
Regular pentagon
f.
Regular hexagon
g.
Star polygon (five- or six-pointed star)
h.
n-gon (you decide the number for n)
Problem C2
a.
What is the relationship between the amount of a turn and the resulting interior angle?
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 different 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 your pencil 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
