Pythagorean Theorem

history and proofs for the classroom

Abstract

Based on data from Saeb and ENEM, it is possible to deduce that the low proficiency in specific geometric skills was not overcome throughout high school and is reflected in the ENEM, as evidenced in the microdata from 2017 to 2022. On the other hand, research with a group of students who had completed elementary school regarding metric relationships in right triangles showed that only 30% recognized the statement of the Pythagorean Theorem. Analysis of mathematics textbooks revealed that the proofs of this theorem are similar, based on algebraic manipulation of metric relationships in right triangles or the decomposition of a specific square. The solution does not appear to be unique, so the scope of this research focuses only on the contributions that knowledge of various ways of proving the Pythagorean theorem can bring to increasing students' geometric skills. In this sense, research was conducted that can be classified, in terms of its approach, as qualitative and, in terms of its procedures, as bibliographic, focused on identifying proofs of the aforementioned theorem and their possible uses in teaching. The objective of this presentation was to demonstrate the Pythagorean theorem at a level of difficulty appropriate for a student completing elementary school. Ultimately, the demonstrations presented can contribute to the teaching and learning processes of the Pythagorean theorem, as well as to the initial or continuing training of mathematics teachers, since they can offer a differentiating factor compared to what is presented in mathematics textbooks.