I'd use a comma in the first and a dash or colon in the second (a comma might make it look like a list with four items in it, not three). Semicolons are right out. They have only two valid purposes (that I can think of, anyway): separating two sentences, and separating items in a list when those items have commas or other punctuation in them already. In the first use, the two sentences could be separated by a period, but the semicolon indicates a closer relationship. Usually, but not always, it could also be replaced with a comma and conjunction.
So yeah, you're right and you're professor's wrong.