No because the teacher has already addressed you with "hello" or "hi". There may be odd occasions when "hi" is not totally correct. Like addressing a Judge with "hi" in a court as an extreme example. It should be "hello"

Hello is never rude. Hi is always fine in informal situations. "Hi" may be slightly less appropriate if you were meeting someone very important or formal. Maybe meeting your boyfriends parents or grandparents for the first time, greeting the president of the company you work for, greeting a judge in their courtroom... In all those cases, Hello is still fine and not at all rude.

As others have already mentioned, it isn't rude. While there are words and phrase that are considered more polite than others in English, it doesn't have different levels of formality or other such constructs like the formal/informal "you" built into the language that others do.

Did somebody told you that it is rude? Actually it's not. Especially if you know the teacher for some time already.

No it isn't rude, as you are just repeating the same greeting that the teacher used to you.