Would this situation be considered plagiarism? - humanities assignment
It is hard for me to see plagiarism here, since you say you used the professor's definition, which is clearly known to both of you.
Of course, it is up to the professor to judge and if the rules are ver strict then perhaps you will be called to account for it.
But you did the right thing in informing the professor of the issue. I'll just have to guess that you are safe.