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I have come across many proofs of Pythagoras theorem like these - enter image description here

But today when i was trying different methods of proving the pythagorean theorem i found a way to prove it. But the construction is so simple and obvious so I wanted to check if this proof is there somewhere - enter image description here

Consider this right triangle with $\angle B = 90°$

$\Rightarrow △ABC \sim △ADB \Rightarrow \dfrac{AB}{AD}=\dfrac{AC}{AB} \Rightarrow AB^2=AC.AD \cdots (I)$

Similarly ,

$△ABC \sim △BDC \Rightarrow \dfrac{BC}{DC}=\dfrac{AC}{BC} \Rightarrow BC^2=AC.DC \cdots (II)$

Adding $(I) , (II) \Rightarrow AB^2+BC^2=AC(AD+DC)=AC^2$. Hence Proved.

A proof so simple yet I never came across it...

Aleph
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  • This site has $100$ different proofs for Pythagoras. Did you look for your proof there? Here is a link to start: Pythagoras, or here. Then check the linked posts at the right side. – Dietrich Burde Jul 30 '22 at 14:25
  • Yes I checked many posts related to pythagoras theorem on this website. Completing the square was the most common proof. – Aleph Jul 30 '22 at 14:27
  • I, at the risk of sounding overly rude, would like to inform you that we, in grade 10, were made to study this proof as a STANDARD PROOF OF PYTHAGORAS’ THEOREM and had to reproduce it in multiple exams. You can check out pages 145-146 here. This proof was purportedly discovered by Einstein(yes, Mr. Albert Einstein of General Relativity fame himself). So you seem to be discovering the same things as him;)… – insipidintegrator Jul 30 '22 at 15:38

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