Generalização do Teorema de Pitágoras por triedro tri-retangular

Abstract

The present work presents different demonstrations of the generalized Pythagorean Theo- rem by the tri-rectangular trihedron. Initially, a brief historical context about Pythagoras, the Pythagorean Theorem and its converse is presented, along with some of its existing de- monstrations, involving geometric, algebraic, and vector approaches. Then, the concepts of the tri-rectangular trihedron and its relation to the theorem are explored, as well as generalizations and applications of the theorem according to some authors. Furthermore, generalizations in three-dimensional space are discussed. The work also analyzes the im- portance of including the generalization of the Pythagorean Theorem in basic education, emphasizing the benefits for the student. The research results will present demonstrations of the generalized Pythagorean Theorem by the tri-rectangular trihedron in different ways. The dissertation concludes by highlighting the relevance of each of the generalizations of the generalized Pythagorean Theorem by the tri-rectangular trihedron, suggesting which one is most suitable for working in high school and which one is most recommended for higher education