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Pythagorean theorem

Pythagorean theorem. Pythagoras discovered the most famous ： 『 a 2 + b 2 = c 2 』 In the right triangle, the squared of the hypotenuse is equal to the sum of the squared of both sides. Pythagorean theorem proof of the oldest. Proof 1. 1.ΔBAF All equal DAC(SAS) 2. Area of ACGF

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Pythagorean theorem

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  1. Pythagorean theorem Pythagoras discovered the most famous：『a2 + b2 = c2』 In the right triangle, the squared of the hypotenuse is equal to the sumof the squared ofboth sides.

  2. Pythagorean theorem proof of the oldest

  3. Proof1 1.ΔBAF All equal DAC(SAS) 2.Area ofACGF ＝2× Area ofΔBAF ＝2× Area ofΔDAC 3. Area ofAMLD ＝2× Area ofΔDAC 4.∴Area ofACGF ＝ Area ofAMLD 5. Same ReasonArea ofBCHK＝ Area ofBMLE 6. ∴ Area ofACGF＋ Area ofBCHK ＝ Area ofABED Scilicet ：AC2＋BC2＝AB2

  4. Proof2 Below left are two large squares of equal area Also lost four identical right-angled triangle Scilicet ：弦2＝勾2＋股2

  5. Problem How to use the three squares to prove thePythagorean Theorem?

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