The present work is dedicated to the study of the theorem of Pythagoras and its contributions in the representations and the demonstrations of exercises of comparisons of areas and of the calculations that represent it, as well as in the constructions that we use in the quotidian, aiming also to familiarize the students of the high school, which often do not give the necessary importance to the study of it. We know that when entering the university to study mathematics one of the first disciplines of the curricular structure is the basic mathematics where the student realizes soon that, compared to what is studied in high school especially in the schools of the public network is another level, soon this begins to feel many difficulties, and inspired in this was done this work. In the course of this work, we will make some applications of the Pythagorean theorem in everyday questions, since we live in a world formed by objects reproduced from geometric forms, and sometimes we do not even realize it, but if we stop to observe, we will soon notice beds, tables, doors, walls, among other objects, that to be constructed with such precision, it was necessary to analyze angles; plus calculations of areas to know the ideal size. But before we talk about the history about the mathematician who gives the name to this theorem, which is Pythagoras, we introduce basic concepts about triangles and two demonstrations of the theorem of Pythagoras.
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