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

Moshe Stupel Shaanan, The religious College of education, Haifa, Israel
David Fraivert Shaanan, The religious College of education, Haifa, Israel

Keywords: Special properties in the trapezoid, Indicator for a trapezoid, Complete quadrangle, Harmonic quadruple.

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.

Downloads

Download data is not yet available.

References

Stupel, M, & Ben-Chaim, D. (2013). A fascinating application of Steiner’s Theorem for Trapezoids-Geometric constructions using straightedge alone. Australian Senior Mathematics Journal (ASMJ), Vol. 27(2), pp. 6-24.

Stupel, M., Oxman, V., & Sigler, A. More on Geometrical Constructions of a Tangent to a Circle with a Straight edge only. The Electronic Journal of Mathematics and Technology Vol. 8(1), pp. 17-30.

Josefsson, M.(2013). Characterizations of trapezoids. Forum Geometricorum,13, pp. 23-35.

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

Oxman, V. & Stupel, M. (2014). Vector algebra as a tool for developing Formulas in the trapezoid. Far East journal of Mathematical Sciences, Vol. 88(2), pp. 241-256Kreger, M, Brindis, CD, Manuel, DM, Sassoubre, L (2007). Lessons learned in systems change initiatives: benchmarks and indicators. American Journal of Community Psychology. doi: 10.1007/s10464-007-9108-14.

Hadamard, J. (2005). Lecons de geometrie elemmentaire, paragraph 194. Ann Arbor , Michigan: University of Michigan, library.