Characterization of a Trapezoid (US) / Trapezium (UK)

The sides a and b are parallel. Click and drag any of the outside vertices. Notice that the blue and red triangles formed by the diagonals always have the same area. Notice that the green and orange triangles are always similar. Notice that the line segment joining the midpoints of the parallel sides always passes through the intersection point of the diagonals. Each of these properties is a characterization that the quadrilateral is a trapezoid (US)/ trapezium (UK).