The properties of straight lines that issue from the point of intersection of the diagonals of a trapezoid, and are perpendicular to its sides

Moshe Stupel, David Fraivert

Abstract


We present four theorems with their proofs, which have to do with the dropping of perpendiculars to the sides of a trapezoid from the point of intersection of the diagonals. Two of the theorems are actually new indicators for the fact that the quadrilateral in which certain characteristics hold is a trapezoid. We also consider whether the converse theorem is also true, as well as different geometric properties that result from the theorems.

Keywords


Special properties in the trapezoid; Indicator for a trapezoid; Complete quadrangle; Harmonic quadruple.

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References


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Fraivert, D. & Stupel, M. (2014). Development and implementation of algebraic formulas for calculation in trapezoids. In the book of the international conference "Mathematical education: current state and future perspectives". Dedicated to the 95th anniversary of Prof. A. A. Stolyar. A. Kuleshov University' Mogilev, Bloruse State. pp. 287-296

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