Question

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

Answer 1

Let use the figure below which represents a right triangle

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.