## Elementary Geometry for College Students (6th Edition)

We have to prove $c^{2} = a^{2} + b^{2}$ on putting given values $a^{2} + b^{2 }= (p^{2}-q^{2})^{2} +(2pq)^{2}$ $= p^{4}+ q^{4}-2p^{2}q^{2}+4p^{2}p^{2}$ $= p^{4}+ q^{4}+2p^{2}q^{2}$ $=( p^{2}+q^{2})^{2}$ $= c^{2}$ hence proved