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. Wikipedia
To construct a Varignon Parallelogram

Create 4 random points (A,B,C,D) on the Drawing Pad.

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>.

Use the midpoint tool to find the midpoint of each side.

Use the segment tool to connect this points, the figure formed is a parallelogram; change these segments to red.

You may move any of the points A, B, C, or D and the interior figure will still be a parallelogram

You can <right-click> on segments to add their value to the display or view it in the Algebra View.

What are the lengths of the opposite side of the midpoint quadrilateral?

What are the slopes if each side of the quadrilateral?

What do these results indicate about this quadrilateral?