Um passeio por alguns tópicos da geometria plana com a utilização do GeoGebra

Abstract

This research encourages teachers and students from public schools to have a differentiated view of geometric entities. We conducted bibliographic reviews of some topics in Geometry that are rarely addressed in Basic Education, but which have significant applicability in solving Olympic problems. Our starting point was the basic concepts of Plane Geometry; we began with the similarity of triangles and later applied a didactic sequence in two ninthgrade classes at a school in the municipality of Juarez Távora-PB. We made use of the GeoGebra software in almost all stages of this didactic sequence and in a large part of this research; our main objective is to use it as a supportive teaching tool for theorem proofs, understanding concepts, visualizing and constructing figures, and developing the didactic product that accompanies this work. Next, we addressed the theorems of the Internal Angle Bisector and the External Angle Bisector and their application, both theorems are very important in solving problems, from the simplest to the most sophisticated. In this context, we explore two other important results, Ceva’s Theorem in its usual and trigonometric forms, and Menelaus’s Theorem, both followed by some applications. Finally, we present the famous Butterfly Theorem with its detailed proof and also give space to inscribable quadrilaterals accompanied by a list of exercises.