Martin Josefsson, Properties of equidiagonal quadrilaterals,
Forum Geometricorum, 14 (2014) 129--144.

Abstract. We prove eight necessary and sufficient conditions for a convex quadrilateral to have congruent diagonals, and one dual connection between equidiagonal and orthodiagonal quadrilaterals. Quadrilaterals with both congruent and perpendicular diagonals are also discussed, including a proposal for what they may be called and how to calculate their area in several ways. Finally we derive a cubic equation for calculating the lengths of the congruent diagonals.

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