NEW APPROACHES TO LEARNING THE TRAPEZE AT SCHOOL

Abstract

The article analyzes theoretical and methodological issues that arise when teaching the concept of a trapezoid in the school geometry course. A comparative review of school geometry textbooks revealed content discrepancies and a lack of consistency in the presentation of material related to trapezoids. In particular, the absence of a precise name for one type of trapezoid and the use of different terms across various textbooks is identified as a significant shortcoming that leads to misunderstanding in the learning process. It is also shown that inconsistencies in the definitions of the trapezoid concept and the differences in how these definitions are formulated hinder deep comprehension of the subject.

From a scientific standpoint, the content, terminology, and classification of any geometric concept must be clearly and accurately defined. Therefore, the aim of the study is to assign a proper scientific name to a type of trapezoid that has remained unnamed in textbooks and to clarify its geometric nature. By considering the trapezoid as a “cut triangle,” new types of trapezoids were identified, arising from cutting a triangle with a line parallel to one of its sides. As a result, the previously unnamed trapezoid type was defined as an “acute-angled trapezoid,” and the concept of an “obtuse-angled trapezoid” was introduced into scientific usage.

The practical significance of the study lies in the discovery of several new properties of trapezoids and the derivation of new formulas for calculating their area based on the new definitions and classifications. These results contribute to the development of geometric science and provide opportunities for improving the methodological system of teaching trapezoids in schools. For the past twenty-five years, innovative mathematics teachers have been successfully applying these findings in educational practice.