How can the Pythagorean Theorem be proved using a mean proportional in a 2-column format?

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Answer 1 · 2015-11-27T23:49:52

Let use the figure below which represents a right triangle

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Using the Leg Rule for the leg labeled "a", we have that

#c/a=a/d=>a^2=c*d# (1)

Using the Leg Rule for the leg labeled "b", we have that

#c/b=b/e=>b^2=c*e# (2)

Now if we add (1)+(2) we get

#a^2+b^2=c*d+c*e=> a^2+b^2=c*(d+e)=c*c=c^2=> a^2+b^2=c^2#

Hence this completes the proof of the pythagorean theorem.