Parallelogram? Why So? (GoGeometry Action 77)

Creation of this applet was inspired by a [url=http://www.gogeometry.com/school-college/p831-quadrilateral-diagonal-midpoint-parallelogram.htm]post[/url] from Antonio Gutierrez ([url=http://www.gogeometry.com/]GoGeometry[/url]). [br][br][b]Feel free to move any of the LARGE POINTS wherever you'd like.[/b][br]The [b][color=#6aa84f]outer green points[/color][/b] control the orientation of the inner white points with which they're collinear.[br][br][b][color=#1e84cc]How can we formally prove that the quadrilateral formed is always a parallelogram? [/color][/b] [br][br]
Quick (Silent) Demo

Information: Parallelogram? Why So? (GoGeometry Action 77)