GEOMETRICAL PROVING METHOD OF PYTHAGOREAN THEOREM

摘要

PURPOSE: A geometrical proving method of Pythagorean theorem is provided to increase the learning will of students instead of unconditional memorizing by proving Pythagorean theorem remaining simply as a theorem. CONSTITUTION: A right-angled triangle for proving Pythagorean theorem has three sides of a, b and c and uses alpha, beta and gamma as inside angles wherein the gamma is 90 degrees and faces the c side. A perfect square is made using the c side as four sides. Each side divided at an angle of alpha and beta from the four angular points is extended inwards the perfect square as long as the side. Four congruent right-angled triangles and a single inner perfect square are formed. Therefore, the perfect square with the c side as four sides is the same width as the sum of all the widths(1,2,3,4,p) of the four congruent right-angled triangles and the single inner perfect square. The Pythagorean theorem is established through the width of the perfect square having the c side as four sides.