Geometria dinâmica: um estudo de atividades investigativas e demonstrações em geometria plana

Abstract

This work aims to constitute a significant way to approach the theorems of Apolônio, Ptolomeu and Euler, present in the book Geometria of the PROFMAT collection. For this, we intend to identify important mathematical and geometric knowledge inherent in the proof of theorems. Aiming at the composition of preliminary investigative activities and the constitution of dynamic geometry applets with the support of the Geogebra software, which can instigate relevant geometric conjectures prior to the theorem demonstrations. Then, for each mentioned theorem we present a demonstration similar to the one shown in the book Geometria of the PROFMAT collection, with the purpose of highlighting passages of the demonstration of the same, in such a way to expose some mathematical arguments that need a significant understanding. Finally, we will present some questions proposed by the same geometry book, which are intended for the direct application of the knowledge acquired in the course of demonstrations and understanding.