Parallelogram In Any Quadrilateral

Inside any quadrilateral (a 4-sided flat shape) there is a parallelogram (opposite sides parallel and equal in length):

When we connect the midpoints (the point exactly half-way along a line) of each side of the quadrilateral, one after the other, we create a new shape that has opposite sides parallel, even though the containing quadrilateral might not.

Play with it here:

To see why, click on the "Diags" button and drag the points around, while thinking "midpoints".

Also try different shape types, such as square and kite, and see what happens.