Pythagorean theorem
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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.
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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 - PowerPoint PPT Presentation
Transcript of Pythagorean theorem
Pythagorean theorem
Pythagoras discovered the most famous ：『 a2 + b2 = c2 』
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 11.ΔBAF All equal DAC(SAS)2. Area of ACGF ＝ 2× Area of ΔBAF ＝ 2× Area of ΔDAC3. Area of AMLD ＝ 2× Area of ΔDAC4. ∴ Area of ACGF ＝ Area of AMLD5. Same Reason Area of BCHK ＝ Area of BMLE6. ∴ Area of ACGF ＋ Area of BCHK ＝ Area of ABED
Scilicet ： AC2 ＋ BC2 ＝ AB2
D E
A B
CF
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L
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< >幾何原本 中畢氏定理的證明
Proof 2Below left are two large squares of equal area
Also lost four identical right-angled triangle
Scilicet ：弦 2 ＝勾 2 ＋股 2
Problem
How to use the three squares to
prove the Pythagorean Theorem?
