Additional trapezoid properties

Abstract

In textbooks elaborated in the Project for the Friendly Learning of Mathematics in Secondary Education in Nicaragua (NICAMATE), enough geometric theoretical aspects are presented to realize a deep study of the trapezoid, however, this is limited to the calculation of area. Therefore, this study proposes to show demonstrations of geometric properties of the trapezoid using the geometry of the triangle and trigonometry, and to provide new properties that relate the elements of an isosceles trapezoid. For this purpose, content analysis, inductive and hypothetical-deductive methods and the authors’ teaching experience are combined. As results, four new ways of demonstration of two known formulas of the area of a trapezoid and a third one in function of the length of its median, the length of a side and the sine of the angle formed by this one and the major base are obtained. In addition, three new demonstrations of a known formula for the length of the median of a trapezoid are presented. Also, formulas not existing in the Spanish-speaking literature that establish relationships between bases, sides and basal angles are deduced and demonstrated. Ratios in a right triangle and trigonometric identities were shown to be useful tools in the demonstration of geometric properties of the trapezoid.