Geometry of Equilateral Triangle Symmetries: A Mathematical Perspective for Teacher Training

Paulo Vitor da Silva Santiago; Francisco Régis Vieira Alves; Maria José Costa dos Santos

Archives · Vol. 13, No. 1 (2025)

Geometry of Equilateral Triangle Symmetries: A Mathematical Perspective for Teacher Training

Paulo Vitor da Silva Santiago, Francisco Régis Vieira Alves, Maria José Costa dos Santos

Paulo Vitor da Silva Santiago — Federal University of Ceara

Francisco Régis Vieira Alves — Federal Institute of Education, Science and Technology of Ceará

Maria José Costa dos Santos — Federal University of Ceará

↓ Download PDF pp. 27–34

Abstract

This article presents a didactic proposal for teaching the symmetries of the equilateral triangle, grounded in Group Theory and the methodology of the Fedathi Sequence. The focus is on exploring the algebraic properties of rotations and reflections mediated by the GeoGebra software, aiming at both the continuing education of mathematics teachers and the initial training of undergraduate students. The proposal seeks to foster visualization, conceptual understanding, and the articulation between Geometry and Algebra. The approach is also based on the Theory of Objectification, emphasizing the active role of the teacher in the construction of knowledge. It is expected that the described experience will contribute to strengthening abstract reasoning through visual and interactive representations.

Keywords: Symmetry groups, GeoGebra, Visualization, Teacher Education

Licensed under CC BY-NC-SA 4.0 · ISSN 2162-3856 · North American GeoGebra Journal