In the GeoGebra applet below,[br][br]1) Select the REGULAR POLYGON [icon]/images/ggb/toolbar/mode_regularpolygon.png[/icon] tool. Then plot 2 points [i]A[/i] and [i]B[/i]. [br] In the pop-up box that appears, enter "3" (without the " "). [br] This creates an "regular triangle" (equilateral & equiangular triangle). [br][br]2) Now use this same tool to construct a regular quadrilateral (square) and regular octagon. [br][br]3) Select the MOVE [icon]/images/ggb/toolbar/mode_move.png[/icon] tool. Move any one (or more) of the [b][color=#1e84cc]blue points[/color][/b] around. [br] Note these polygons always remain regular. [br][color=#0000ff][br]When you're done (or if you're unsure of something), feel free to check by watching the quick silent screencast below the applet.[/color]
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.