2023-12-052023-12-052023-12-052023-10-10https://repositorio.ifal.edu.br/handle/123456789/335The purpose of this study is to present a brief historical approach to the Pythagorean Theorem and its metric relations, who derive from it, and to present a didactic proposal using manipulative didactic material. Understanding of concepts related to metric relations, through the interaction of geometric construction with algebraic development. Difficulties related to solving mathematical problems in basic education are known. It is believed that the lack of understanding of basic concepts is defining when it comes to learning. In this line of reasoning, the interaction between algebraic development and geometric construction will be used, seeking to understand specific theorems related to metric relations of the right triangle and their applications in everyday life. In our discussion, we will emphasize the metric relationships and the existing relationship between the square of the leg and the product of the hypotenuse by the projection of that leg, always seeking to highlight the concept of area, due to its importance in solving practical everyday problems. We aim for this approach to facilitate, both students and teachers, the understanding of the geometric concepts that determine these relationships and not rely only on ready-made “formulas”. It is hoped that our discussion can provoke reflections in relation to the teaching practice of future mathematics teachers. And that will also contribute to the differentiated training of undergraduate students in Mathematics, collaborating with a closer relationship with the academic reality of the students.Acesso AbertoMaterial manipulávelRelações métricasTeorema de PitágorasTriângulo retânguloManipulable materialMetric relationsPythagorean TheoremRight triangleTrabalho de Conclusão de CursoCIENCIAS EXATAS E DA TERRA