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

Let use the figure below which represents a right triangle

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

$\frac{c}{a} = \frac{a}{d} \implies {a}^{2} = c \cdot d$ (1)

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

$\frac{c}{b} = \frac{b}{e} \implies {b}^{2} = c \cdot e$ (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.