The three angles of triangle A have measures $\(90, x\)$ and $\(y\)$, so we get $\(90+x+y=180\)$ which gives $\(x+y=90\)$. $\(\qquad\)$

Also the three angles of triangle $B$ have measures 90 , $\(z\)$ and $\(w\)$, so we get $\(90+z+w=180\)$, which gives $\(\mathrm{z}+\mathrm{w}=90\)$. $\(\qquad\)$

Now, checking from the statements we have

I. $\(x-w=z-y\)$ i.e. $\(x+y=z+w\)$, which is true using (1) \& (2).
II. $\(x+y=w\)$, which cannot be true as we have $\(x+y=w+z\)$
III. $\(z=90-w\)$ i.e. $\(z+w=90\)$, which is true using (2).

Hence statements \(I \& III \)are true, so the answer is (C).