S_{hình thang}  = \(\dfrac{\left(a+b\right)\left(a+b\right)}{2}=\dfrac{\left(a+b\right)^2}{2}\)

Lại có S_{hình thang \(=\dfrac{ab}{2}+\dfrac{ab}{2}+\dfrac{c.c}{2}=\dfrac{2ab+c^2}{2}\)}

_{=> \(\dfrac{\left(a+b\right)^2}{2}=\dfrac{2ab+c^2}{2}\Leftrightarrow\left(a+b\right)^2=2ab+c^2\Leftrightarrow a^2+2ab+b^2=2ab+c^2\Leftrightarrow a^2+b^2=c^2\)} (đpcm)