Perpendicular Lines Generated by a Quadrilateral

The centroid of a triangle is the intersection of the lines drawn from the vertices to the midpoints of the opposite sides.

The orthocenter of a triangle is the intersection of the altitudes.

Let ABCD be a quadrilateral. Let O be the intersection of AC and BD. Draw lines between the centroids of AOB and COD and the orthocenters of BOC and DOA. Those lines are perpendicular.