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.[more]
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.[less]