The way to do it can be explained like this: Say AB and CD are the two parallel lines cut by a transversal at E and F respectively.
Then the pairs of alternate interior angles are:
Angle(AEF) and Angle(DFE)
Angle(CFE) and Angle(BEF) Now lets prove if this is true: Angle(CFE) +Angle(DFE) = 180
(linear pair)
Also Angle(CFE) +Angle(AEF) = 180 (Corresponding angles) Equate the above results:
Angle(CFE) +Angle(DFE) = Angle(CFE) +Angle(AEF) Angle(DFE) = Angle(AEF) Happens the same with Angle(CFE) = Angle(BEF) Hope this is very useful for you
