Geometrization of the Pythagorean Theorem and its generalization as Polya's Theorem
DOI:
https://doi.org/10.23925/2237-9657.2025.v14i1p058-075Keywords:
Pythagorean theorem, Geometry, Polya theorem, AreasAbstract
Pythagoras Theorem is considered one of the most important and well-known theorems in Mathematics due to its wide applications in solving problems related to geometry and to sciences. Currently, in most situations, especially in Basic Education, its approach occurs essentially via its algebraic form, with little emphasis on geometry. The article, which is part of a master's thesis, aims to present an approach to prove Pythagoras Theorem focusing on its geometrization, using areas of similar figures, via constructions performed by the GeoGebra software. Additionally, it presents a proof and interactive constructions of Polya's Theorem, which is one of the generalizations of the Pythagoras Theorem. Such approach may arouse more interest in these results, as they provide a significant conceptual and visual understanding of the theorems, instead of their purely algebraic versions.
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