Well I don't remember any of the actual wordings of the theorems but anyway...
2) I think this is the Alternate exterior angles theorem
3) I don't remember but you can prove that the angles are congruent and then show the lines to be indeed ||
4) Alternate interior angles or something like that - if lines || and cut by trans. then the angles add up to 180 degrees
5) I would show that both lines have the same slope and are thus ||
If you need the reasons for number one let me know