I was reading Euclid's Elements E-book I found online and got stuck on this concept. I will just copy what I found to be very absurd.
There could still be another different triangle with the same sides. [For instance there are usually two different triangles with the same SSA data, but they are not close to each other, so you cannot wobble one into the other. So showing that a triangle cannot wobble when certain measurements are fixed only suggest there are only a finite number of such triangles, it does not really argue there is only one.]
I don't really understand what he's saying here... What does it mean when triangles wobble? I just can't picture another different triangle also has same sides.