May I say: "The jackal relates to the dog as the tiger to the cat"? Or must it be "corresponds", or anything else?
The way this is typically expressed in English is simply by using the verb is:
The jackal is to the dog as the tiger is to the cat.
Personally, I'd avoid using relates. When I read:
The jackal relates to the dog...
I imagine the two animals conversing somehow (perhaps over a card game or something). It's not ungrammatical; it's just not usual.