Carlos+Barrera

=**__Pythagorean Theorem Proof__**=

===The Pythagorean Theorem was known over 1000 years prior to Pythagoras being born, but he was the first person to discover the proof for it. The Pythagorean Theorem states, that in a right triangle with sides a, b, and hypotenuse c, then c^2 = a^2 + b^2. There are many proofs to the Pythagorean Theorem, and this is probably the most famous of proofs, because it's the first of Euclid's two proofs.===

<BAF = <BAC + <CAF = <CAB + <BAE = <CAE.
===∆ABF has bas AF and the height AB is equal to AC, so its area must equal half of the square with side AC. ∆AEC has base AE, and the height AC is equal to AM, while point M is the point of intersection of AB and line CL is parallel to AE. Thus the area of ∆AEC equals half the area of the rectangle AELM, which means because ∆ABF = ∆AEC, the area of square AC^2 equals the area of the rectangle AELM. Similarly the area of the square BC^2 = the area of the rectangle BMLD, and finally the two rectangles AELM and BMLD make up on the hypotenuse AB for ∆ABC.===

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