Resolução de problemas de geometria euclidiana utilizando técnicas de geometria projetiva

Abstract

The present dissertation aims to show the applicability of techniques from Projective Geometry in solving Euclidean Geometry problems. Initially, a parallel is drawn between the two geometries and a historical contextualization of Projective Geometry is made. Next, Euclidean versions of definitions, propositions and theorems from Projective Geometry are presented. Finally, problems of Euclidean Geometry are solved using techniques of Projective Geometry. This approach gives the students an alternative way to solve geometric problems, especially in mathematical Olympiads.