/sci/ - Science & Math

So, I'm really bad at proving things in geometry, so I'd like to know if this is right:
BOA + AOD = BOD = 180º
AOD and AOB are supplementary
AOD + DOC = AOC = 180º
AOD and DOC are supplementary
AOD and BOC are vertical angles since the sides of one of them form continuations of the sides of the other(Lines AC and BD)
AOD = BOC
E is bisector of AOD and F is bisector of BOC
AOE + EOD = AOD
BOF + FOC = BOC
BOA + AOE + EOD = BOD = 180º
AOB + BOF + FOC = AOC = 180º
AOE + EOD = BOF + FOC
AOE - BOF = FOC - EOD
AOE = BOF = FOC = EOD(since lines E and F are bisector of congruent angles)
As proved here:
AOB + BOF + FOC = AOC = 180º
and since FOC = AOE:
AOB + BOF + AOE = EOF = 180º
Ergo, E and F are continuations of each other.

Now, would someone know any good book that helps get good at proving things in geometry? One that has a great focus in developing skills in proof and whatnot. This is the only thing in geometry that kills me every time.