Given segments $a$ and $b$. Construct the segments $\sqrt{a^{2}+b^{2}}, \sqrt{a^{2}-b^{2}}$.
The segment $\sqrt{a^{2}+b^{2}}$ - the hypotenuse of a right triangle with legs $a$ and $b$.

The segment $\sqrt{a^{2}-b^{2}}$ - the second leg of a right triangle with hypotenuse $a$ and leg $b$.