Banca de DEFESA: RONIVON ALVES

A STUDY OF TRIANGLES: FUNDAMENTAL PROPERTIES AND RELATIONSHIPS

Geometry. Triagle. Relational Operator.

From ancient to modern times, triangles have sparked curiosity and signicant interest in the search for mathe-

matical relationships and inherent properties of that polygon. As its title suggests, this study aims to investigate 

triangles and the main relationships among their elements, serving as a resource for deeper exploration of the 

topic by students and teachers in basic education. Initially, we surveyed how the topic has been addressed in 

textbooks approved by the National Textbook Program (PNLD) and then conducted a theoretical study on the 

subject. We observed that, in exploring this theme, a recurring expression emerges: (a²+b²−c²), where a, b, and

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c are the side lengths of a triangle, which, in this study, we define as the triangular relational operator. Defining 

such expression allows us to rewrite well-known equations, such as Heron's formula, in a dierent form and to 

simplify expressions involving triangular elements, making them easier and more practical to manipulate, as we 

demonstrate throughout this study.