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Perpendicular Lines Generated by a Quadrilateral

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

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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.

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Contributed by: Jay Warendorff (March 2011)
Open content licensed under CC BY-NC-SA

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