If two lines are parallel, they do not intersect -- this one is true. the definition of parallel lines prevents these lines from crossing one another, because at that point they would no longer be parallel. parallel lines never touch.
If two lines do not intersect, then they are parallel -- not necessarily. skew lines are the exception here. you probably won't touch on it at your current level of math, but lines exist in higher dimensions than the second (third dimension, fourth dimension, etc) that prevent this from being necessarily true. if your class is ONLY related to two-dimensional geometry and your teacher doesn't want you to consider higher dimensions, then there's no reason to use this answer; the statement would be true.
