1. 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.

2. Pythagorean theorem proof of the oldest

3. Proof 1 1. Δ BAF All equal DAC(SAS) 2. Area of ACGF ＝ 2× Area of Δ BAF ＝ 2× Area of Δ DAC 3. Area of AMLD ＝ 2× Area of Δ DAC 4. ∴ Area of ACGF ＝ Area of AMLD 5. Same Reason Area of BCHK ＝ Area of BMLE 6. ∴ Area of ACGF ＋ Area of BCHK ＝ Area of ABED Scilicet ： AC 2 ＋ BC 2 ＝ AB 2

4. Proof 2 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 the Pythagorean Theorem?