An interesting theorem related to a hexagon with opposite sides that are parallel

Abstract

ABSTRACT It’s often useful extending students beyond the limiting geometry of triangles and quadrilaterals to regularly consider generalizations of results for triangles and quadrilaterals to higher order polygons. A brief heuristic description is given here of the author applying this strategy, and which led to an interesting result related to the perpendicular bisectors of a hexagon with opposite sides parallel, and a rather novel proof. It provides a nice challenge and exploration for students to investigate using dynamic geometry.