Question

how can we identify if a given line is parallel or not

Answer 1

you can identify that when Two lines do not intersect at any point, then they can be said as Parallel Lines. You can also represent that bt llel.

Answer 2

we can prove that fig. to be in conditions which are used in parallel lines
ex. corresponding angles or alternate interior angles.. once it is proved that there is alt. int. ang or corresponding angles ar3 occuring, then the lines will be parallel....
hope this will be helpful.. in doubt, ask me then