Below is a right triangle \[\triangle MNO\] where \[MO=a\], \[ON=b\], and \[MN=c\]. An altitude \[\overline{OP}\] is constructed so \[MP=x\] and \[PN=y\]. Triangle M N O where no angles are congruent. Side M O is A units long. Side O N is B units long. Side N M is C units long. Point P lies on side N M so that segment O P is the altitude of the triangle, segment M P is X units long, and segment P N is y units long. \[M\] \[N\] \[O\] \[P\] \[a\] \[b\] \[x\] \[y\] \[c\] Triangle M N O where no angles are congruent. Side M O is A units long. Side O N is B units long. Side N M is C units long. Point P lies on side N M so that segment O P is the altitude of the triangle, segment M P is X units long, and segment P N is y units long. Below is the proof of the Pythagorean theorem, that \[a^2+b^2=c^2\]. The proof is divided into three parts, where the title of each part indicates its main purpose. Complete part C of the proof. Part A: Prove \[a^2=c\cdot x\] [Show the steps.] Part B: Prove \[b^2=c\cdot y\] [Show the steps.] Part C: Prove \[a^2+b^2=c^2\]