Resolução de triângulos e suas congruências: uma proposta didática para o ensino médio utilizando o geogebra

Abstract

Geometry has been studied throughout human history by various peoples, each of whom has developed methods for solving problems involving areas of different plane figures such as triangles. In the 21st century it is already possible to solve mathematical and geometric problems using digital technologies. The objective of this work is to carry out a bibliographical research on the subject: solving problems with triangles and their congruences, in search of theoretical foundations to build a didactic proposal for teaching plane geometry, with the help of Geogebra as an educational resource, to improve the learning of high school students. The use of digital technologies for teaching mathematics and its languages according to the normative orientations of Brazil, through information technology, is considered as important, aiming at overcoming didactic obstacles between teachers and students. The methodology for achieving the objective is qualitative and was developed through bibliographic research and internet research to support the applied perspective. The procedures are found in a literature review that addressed three aspects, the history of plane geometry, plane geometry and the teaching of plane geometry in high school, as well as the state of knowledge about academic production in Brazil on the subject, highlights in this production, the use of Geogebra is used, software that has tools that allow approaching various contents of mathematics, especially geometry, and which will be used in the didactic proposal. This proposal has in its composition a didactic sequence of five classes of approximately 45 minutes each, on the contents of law of sines, law of cosines and cases of congruence between triangles. It is considered that this monograph can contribute to Basic Education teachers who want to apply the proposal, as it brings together a bibliographic review and other studies on the subject in a single space, in addition to collaborating so that High School students can improve their learning about geometry flat using GeoGebra in their studies on solving problems with triangles.