Everybody knows that A² + B² = C² but are you able to prove it?-The Pythagorean Theorem is known by someone who has taken basic geometry. In a right triangle, the square of the hypotenuse is equal to the sum of the squares of both legs.
Fortunately has not one, not one but eighty ways that the Pythagorean Theorem has been proved over the years. You could spend five months learning a proof a day, but this is my favorite.
Most people know that the area of a rectangle is determined by multiplying base times height. The area of the blue square, then, is the hypotenuse of one triangle multiplied by the hypotenuse of the other. Since all the triangles are the same, the area of the blue square is the length of the hypotenuse squared.
The square on the right shifts the triangles around, leaving one red squares visible. The area of the tiny upper red square is defined on all sides by the short side of the triangles, so it can be expressed as length of the short side squared. The area of larger, lower red square is defined on all sides by the longer side of the triangles, so it can be expressed as the length of the long side squared.
Shifting things around doesn't give them a bigger or smaller area. In other words, the non-yellow area of both squares is the same, or equal.
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