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It worked, didn't it? You just fitted the area of the squares along the legs into the square along the hypotenuse.
This relationship has been known for a long time. Pythagoras is said to be the first to have proven that it works in all right triangles. Since then it is called the Pythagorean theorem.
Pythagorean theorem: In a right triangle the square of the measure of the hypotenuse is equal to the the sum of the squares of the measures of the legs.
or in the arithmetic form:
If a and b are the legs of a right triangle and c is its hypotenuse, then a2+b2=c2.
Below is a simple proof for the Pythagorean theorem.
