Cevianas e pontos associados a um triângulo: uma abordagem com interface no ensino básico

• Ano de defesa: 2014
• Autor(a) principal: Araújo, Genaldo Oliveira de
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal da Paraíba; Brasil; Matemática; Mestrado Profissional em Matemática; UFPB
• Palavras-chave em Português: Ensino da geometria; Cevianas; Pontos e triângulos; Geometry teaching; Ceviana; Points and triangles; MATEMATICA::MATEMATICA APLICADA
• Link de acesso: https://repositorio.ufpb.br/jspui/handle/tede/9403

We have developed this work to contribute positively to teaching of geometry in basic education form, because although this branch of mathematics is very important in the training of students is very underprivileged in this phase of education. Through him, we mentioned some factors that can in uence in the context in which it is teaching geometry, aiming to serve as a re ection and a possible repositioning apposite situation. We also made a simple approach to deductive and reasoning and the axiomatic method primary education, taking into account the importance of this method in the study of geometry that stage. To develop skills in geometry while giving consistency to certain content in basic education, and more precisely on cevianas associated with a triangle, we have created an axiomatic model, through we approach simply some classic de nitions and theorems of Euclidean Geometry, some of them being common in primary education, and others, not so much. So they are: Menelaus's Theorem, Ceva's Theorem, Stewars's Theorem, the four notable points of the triangle (orthocenter, circumcenter, incenter and the centroid), Euler Line, Nine - Point circle, Euler Point, Gergonne Point, Nagel Point, Feuerbach Point, as well as introduce the de nition of isotomic points, isotomic straights and reciprocal points. In the theorems, we use only elementary methods of Synthetic Geometry, becoming a subject easy to understand that can be exploited in basic education. We believe the focus of the structure of this work can serve as a motivation for students and primary school teachers seeking to improve their knowledge of geometry.