In Chapter 1 of Spivak's Calculus (3rd Edition), problem 3, number (vi) it asks us to prove the following:
If $b,d \ne 0$, then $$\frac{a}{b} = \frac{c}{d} \iff ad = bc.$$ Determine when $\dfrac{a}{b}=\dfrac{b}{a}$.
So far, I have been able to prove all questions from this problem, but I really do not know how I should approach this one, when a proof gives me an iff. I have only worked on proofs of the form $p \implies q$.
I am not asking here to get a solution that I could copy to my notebook. I am sincerely interested on how should I do this proof since I am clueless about it. I hope someone can help me.