Geometrização do teorema de Pitágoras e sua generalização como o teorema de Pólya.

Abstract

The Pythagorean Theorem is considered one of the most important theorems in Mathematics, due to its wide application in solving problems related to Geometry and related sciences, mainly to calculate distances. Currently we realize that the Pythagorean Theorem is being presented to students, especially in Basic Education, in its algebraic format, with little emphasis on Geometry and sometimes students do not understand its geometric meaning. In this research, we approach the Pythagorean Theorem in a fully geometric format, using areas of similar gures. In addition, we will present Pólya’s Theorem, in a more formal version that we commonly nd, as one of its generalizations. For this, we will approach important concepts of Plane Geometry that are essential for the understanding of these theorems, such as similarity of gures and areas. We also present suggestions for didactic sequences to be applied in 9th grade and 1st grade classes of Basic Education and we develop dynamic activities using the GeoGebra software to show the theorems of Pólya and of Pythagoras through areas.