Prove surfaces $\sigma_1$, $\sigma_2$ are not isometric.

One of my homework problems gives me two surfaces $\sigma_1$ and $\sigma_2$ and asks me to show that they are not isometric to each other. I was wondering what my approach should be in proving such a statement.

I was thinking of showing that they have distinct first fundamental forms, would that be enough? am I mistaken to think so?

-
 It's better to give us more information about $\sigma_1$ and $\sigma_2$ so that we can help. – Paul Dec 16 '12 at 1:11