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I've been wondering about this for years. It seems like a pretty obvious question, so I'm surprised not to have found it addressed among the other Tolkien minutiae on this site. Hopefully I haven't missed it, but anyway, here goes...
In Tolkien's Middle-Earth writings, Evil cannot create things, only twist and warp what already exists. Thus, Orcs are twisted Elves, Trolls are twisted Ents, etc. So then, what's the original source for Dragons? They look pretty original to me!
The only template that seems even remotely possible is the Eagles, as they're both powerful fliers, but the connection seems very remote indeed. Also, as twisted copies Orcs and Trolls are markedly inferior to Elves and Ents respectively, but I'm not aware of any text describing Dragons as inferior to Eagles.