Generalisation of a quadrilateral duality theorem

Abstract

We will prove a generalisation to our Theorem 10 about duality between orthodiagonal quadrilaterals and equidiagonal quadrilaterals in [1, p. 134]. These are quadrilaterals with perpendicular diagonals and diagonals of equal lengths respectively. Unfortunately we made a careless mistake in the proof of Theorem 10 (ii) in [1], which was found by Zoltán Szilasi at the University of Debrecen in Hungary. When reviewing that theorem, we realised that it's just a special case of a more general theorem. The equilateral triangles in Theorem 10 can be replaced by almost any regular polygons.