We've just started congruency in my class, and we've stumbled across a question which goes like this:
Prove that ∆AOB $\equiv$ ∆COD
I drew up a diagram which portrays exactly the same information yet makes it impossible to prove that $\angle$AOD = 180°.
I would assume that they are straight lines, because, as you said, it is false if you assume otherwise.
However, usually some text describing the construction of the figure is nearby, and it would tell you something like "Let O be the intersection of lines AD and BC".