Given: Triangle ABC is isosceles with AC congruent to BC.
AC is extended to D.
Prove: AD > DB
It's Problem #3 on page 2:
Does this help?
I gave you the general solution. There is usually a theorem that states: In a triangle, if two angles have different measures then the longer side is opposite the larger angle. Now there are all sorts of ways to prove that. BUT each way depends upon the particular axiom set in use. We have no way to know that.