Regular Polygon Phenomena!

Shown in the applet below are a [b][color=#38761d]regular pentagon[/color][/b], [color=#bf9000][b]regular hexagon[/b][/color], and [color=#666666][b]regular decagon[/b][/color]. [br][br]The 2 LARGE VERTICES of the [b][color=#38761d]regular pentagon[/color][/b] can be moved anywhere you'd like at any time. [br][br][b][color=#9900ff]How can we formally prove the phenomena dynamically illustrated here? [/color][/b]
Quick (Silent) Demo

Information: Regular Polygon Phenomena!