Is a works cited page necessary here?

You don't have to do a works cited. If you're doing it off the top of your head and not researching it that means that you're doing it from the stuff that you've already learned. You couldn't have learned it from nowhere, so there's always going to be some source of your knowledge, in this case you aren't going to have to do a works cited. You should really just ask your teacher to be sure, though.