Volume no :38, Issue no: 1, March

Journal of Mathematical Sciences: Advances and Applications

COMMON PROPERTIES OF TRAPEZOIDS AND CONVEX QUADRILATERALS

Author's: David Fraivert, Avi Sigler and Moshe Stupel
Pages: [49] - [71]
Received Date: February 24, 2016
Submitted by:
DOI: http://dx.doi.org/10.18642/jmsaa_7100121635

Abstract

In this paper, we show some interesting properties of the trapezoid which have to do with the perpendiculars that issue from the point of intersection of the diagonals to non-parallel sides. For each property that will be proven for the trapezoid, a check shall be made with regards to the extent to which this property is retained in a quadrilateral that is not a trapezoid. At the same time, it is suggested and backed by a proof that some of the properties which hold true for the trapezoid also hold true for any convex quadrilateral, but their proof requires college-level knowledge. The paper illustrates the method of investigation “what if not”, which permits guided investigations to be carried out.

Keywords

trapezoid, convex quadrilateral, harmonic quadruplet, the Appolonius circle, minimal perimeter, the complete quadrilateral, the homothety transformation, Menelaus’ and Ceva’s theorems.