Geometria: explorando a relação entre o teorema de Napoleão e a semelhança de triângulos

Abstract

This work aims to investigate the relationship between Napoleon's theorem and the similarity of triangles, in order to make them more accessible and understandable in the context of geometry teaching. For this purpose, a qualitative research was carried out, with an exploratory and descriptive approach, based on bibliographic review and geometric analysis through constructions made with the GeoGebra software. The study demonstrated that it is possible to use the criteria of triangle similarity as a basis to justify the formation of Napoleon's triangle, whose construction involves equilateral triangles associated with the sides of any given triangle. The results showed that this approach favors mathematical visualization and reasoning, in addition to expanding the didactic possibilities in geometry teaching. It is concluded that the integration between classical theorems and fundamental contents, such as similarity, can enrich and significantly enhance the teaching-learning process, promoting more meaningful connections between theory and practice.