The Three Elven Rings

[Alchisiel]

I've been thinking about the 3 elven rings...if Sauron didn't have a hand in their making why did the rings lose their power with the destruction of the One ring? That doesn't make sense to me. I would think that since Sauron didn't make them and had nothing to do with making them why would the destruction of the master ring bring the destruction of the other rings? The only thing I can think of is because Sauron instructed the elves in their craft of making all of the rings that the others can be destroyed, or that because he crafted the One to master all other rings their fate was tied to his, but then this doesn't really make sense to me either. Any thoughts?