I'm having difficulty proving the following question. I know it's true, but I don't know what exactly to use.
Let D on BC of triangle ABC so that D bisects angle BAC. Prove that AB >AC if and only if DB>DC.
Consider using the Law of Cosines ( https://en.wikipedia.org/wiki/Law_of_cosines ) and apply it to triangle ABD and triangle ACD to express BD^2 and CD^2. From here, you should be able to prove both directions of the if and only if statement.
Let me know if you have further questions.
Greetings from Calgary.