Answer
Pythagorean Theorem is verified.
Work Step by Step
Given the vectors ${u}=(1,-1), \quad {v}=(1,1)$, then their lengths can be calculated as follows
$$\|{u}\|^2=1+1=2, \quad \|{v}\|^2=1+1=2.$$
Since $u+v=(2,0)$, then
$$\|{u+v}\|^2=4+0=4.$$
One can see that,
$$\|{u}+{v}\|^{2}=\|{u}\|^{2}+\|{v}\|^{2}$$
Hence, Pythagorean Theorem is verified.