Inequalities in Triangles

Firstly, you guys must be wondering how come all threads started by me are always in the 'Urgent Homework Help' section. Well, that's me.... I always get reminded of homework a li'l late.

Secondly, Inequalities in Triangles is a topic I find difficult to understand at all. So, I'd kindly request you people to please post all the steps. Please! I understand the theorems of inequalities, however, I fail to be able to apply in the sums.

1. In triangle ABC, if AD is a median, prove that AB + AC > 2AD

2. In triangle ABC, AB > AC. From the greater side AB, AD is cut off equal to AC and DC is joined. Prove that -

i) Angle ACD = 1/2 (Angle B + Angle C)

ii) Angle BCD = 1/2 (Angle C - Angle B)

Thanks a lot! Thanks!