[color=#c51414]The midpoints of the sides of an arbitrary quadrangle form a parallelogram. If the quadrangle is convex or reentrant, i.e. not a crossing quadrangle, then the area of the parallelogram is half as big as the area of the quadrangle.[/color] [url=http://en.wikipedia.org/wiki/Varignon%27s_theorem]Wikipedia[/url][br][br]To construct a [b]Varignon Parallelogram[/b][br][br][list][br][*]Create 4 random points (A,B,C,D) on the Drawing Pad.[br][*]Using the segment tool connect the points A,B,C,D,A to form a quadrilateral; change the color of these segments to blue by selecting properties with a <right-click>.[br][*]Use the midpoint tool to find the midpoint of each side.[br][*]Use the segment tool to connect this points, the figure formed is a parallelogram; change these segments to red. [br][/list][br][br]You may move any of the points A, B, C, or D and the interior figure will still be a parallelogram