Regular Polygons
DIRECTIONS:
In the GeoGebra applet below,
1) Select the REGULAR POLYGON 
tool. Then plot 2 points A and B.
In the pop-up box that appears, enter "3" (without the " ").
This creates an "regular triangle" (equilateral & equiangular triangle).
2) Now use this same tool to construct a regular quadrilateral (square) and regular octagon.
3) Select the MOVE 
tool. Move any one (or more) of the blue points around.
Note these polygons always remain regular.
When you're done (or if you're unsure of something), feel free to check by watching the quick silent screencast below the applet.
tool. Then plot 2 points A and B.
In the pop-up box that appears, enter "3" (without the " ").
This creates an "regular triangle" (equilateral & equiangular triangle).
2) Now use this same tool to construct a regular quadrilateral (square) and regular octagon.
3) Select the MOVE tool. Move any one (or more) of the blue points around.
Note these polygons always remain regular.
When you're done (or if you're unsure of something), feel free to check by watching the quick silent screencast below the applet.Quick (Silent) Demo
Generalize your work above my creating a slider n with min 3, max 12, and increment 1. Then use the Angle with Given Size tool to create an angle of size (360 degrees)/n. Select the Regular Polygon tool and then click on vertex A and A' to construct a regular n-gon (Vertices = n) controlled by slider n.
What happens to the regular n-gon's central angle as n increases?
Select the Angle tool in the window above and click somewhere inside the regular n-gon. You should see the interior angles. Move slider n to see how the regular n-gons' interior angles change. Write any patterns you notice.