Question

are all coplanar lines parallel?

Answer 1

not necesarly

Answer 2

Are all lines in the x-y PLANE parallel? :P

Answer 3

no

Answer 4

Answer to your question then :P Only need 1 counter example :P

Answer 5

good example @malevolence19 .
@berenicechavez - coplanar just means they lie in the same plane - which means they may or may not be parallel.