Traçados geométricos auxiliares em triângulos: descrição de técnicas e produção de material de ensino e aprendizagem em impressora 3D

Abstract

This work is the result of research on auxiliary constructions in triangles. The main objective was to investigate literature on teaching and learning geometry for Basic Education on this topic; as a consequence, a kit was produced for use in a Mathematics laboratory dedicated to teaching and learning Geometry. We organized and presented the techniques of auxiliary constructions in triangles, describing them as propositions – created specifically for this work – and demonstrating them in language suitable for Basic Education students. Furthermore, we provided solutions to problems using these techniques. We selected specific questions to compose the kit developed during this research, with the assistance of the freely distributed software Blender, which we named “3D Printer Mathematics Kit: Geometry Problems with Auxiliary Constructions in Triangles”. This educational kit will be made available for free on digital platforms for educational resources, aiming to promote the study of geometry and encourage teachers to create pedagogical materials that facilitate the learning process. The kit was designed so that students can solve geometry problems without relying on conventional materials such as notebooks and pens; instead, they assemble the pieces that form the figures for each problem and discuss angle measurements and congruences of segments and triangles within a group. We hope to contribute to Mathematics classes and foster a maker culture in the school environment, empowering teachers to create materials for mathematics laboratories in schools.