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The Pythagorean Theorem: History and cases for triangles not rectangles, with sight to teachers of basic and average education

Abstract:

Our goal is to make a historical and geometric presentation of the Pythagorean Theorem, different from the algebraic presentation that a large number of primary and secondary school teachers usually perform, which makes the student forget it quickly. Observing the Theorem in a geometric way, we present simple examples to motivate in students a logical deductive thinking, without the need to know the irrational numbers or calculate square roots. Also, we will show a geometric version for triangles not rectangles (acute and obtuse triangle), its history and examples with positive integers of easy application.