math problems HELP~!!

(a) To prove ∠ABE = ∠CDF:

∠ABD=∠CDB (alt. ∠s, AB//CD)
∠ABE+∠ABD=180 (adj. ∠s on st. line)
∠ABE=180-∠ABD
∠CDF+∠CDB=180 (adj. ∠s on st. line)
∠CDF=180-∠CDB
∠CDF=180-∠ABD=∠ABE

(b) To prove EA//CF:
Comparing triangle EAB and triangle FCD
EB=DF (given)
∠ABE = ∠CDF (proved in (a))
AB=CD (given)
so triangle EAB (~ =)(congus.) triangle FCD

∠BEA = ∠DFC (corr. ∠s, ~= trianlges)
so EA // CF (alt. ∠s equal)

a)
draw CD upwards longer and let G be on the produced line
∠ABE = ∠BDG
∠BDG = ∠CDF
so, ∠ABE = ∠CDF

b)
EB = DF (given)
AB = CD
and ∠ABE = ∠CDF

triangle ABE and triangle CDF are congruent
∠AEB = ∠CFD
so, EA // CF