Suppose you take two sticks (not necessarily of the same lengths), hinge them at a common end, and attach a rubber band at the other ends.  Then you can open and close them to form triangles as the following illustrates: 

When comparing two triangles with two pairs of congruent sides, you see that the triangle with the larger angle between those sides has the larger third side, and conversely:

This result is known as:

The Hinge Theorem

If in  and ,  and  then  if and only if .

The result is rather obvious if you think of the rubber band idea, and we will not prove it here.  Instead we will consider some examples.