I am answering the first question.
1) AD = CD --> given
2) ∠ADB = ∠CDB --> given
3) BD= BD -- > reflexive property
4) ΔADB ≅ ΔCDB -- > SAS congruence (lines 1, 2, 3)
5) AD≅CB -- > CPCTC
Sorry about the format. =) Your welcome.
CPCTC --> Congruent Parts of Congruent Triangles are Congruent
SAS --> Side Angle Side