Prove the Following:

Question

Given: AD = CD, ∠ADB > ∠CDB

Prove: AB > BC

Answer 1

IF 2 triangles have 2 sides of one equal respectively to 2 sides of the other but the included angle of the first triangle is greater than the included angle of the 2nd, then the third side of the first triangle is greater than the 3rd side of the second.

The proof of this theorem is too messy to duplicate here, but check in a classical geometry book to follow the proof.