Elementary proof of a theorem about hexagons with parallel opposite sides

• Autores: Rolfdieter Frank, Heinz Schumann
• Localización: International journal of mathematical education in science and technology, ISSN 0020-739X, Vol. 54, Nº. 10, 2023, págs. 2304-2308
• Idioma: inglés
• DOI: 10.1080/0020739X.2023.2243944
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• Resumen

  • The perpendicular bisectors of the sides of a hexagon, whose opposite sides are parallel, produce a point symmetric hexagon. Michael de Villiers already gave two proofs of this theorem, firstly an elaborate one with the aid of dynamic geometry and secondly a merely verifying one with the help of coordinates and computer algebra. In this note, we present a short elementary proof. Our proof uses the fact, that the three altitudes of a triangle intersect in a common point, and it also covers degenerate cases.