Yes. US copyright law includes a Classroom Use Exemption (17 U.S.C. §110(1)) that gives teachers broad rights to show movies to students during in-person teaching at a nonprofit educational institution. No special permission needed. The main conditions are that it has to be in a classroom setting, in person, as part of teaching, and the copy being shown must be a legally purchased or rented one. If those boxes are ticked, you're covered.
Teachers outside the US are similarly protected in most countries. The UK's Copyright, Designs and Patents Act 1988 (Section 34) covers classroom movie use under the same principle. Most developed countries have equivalent educational exemptions built into their copyright law, though the specifics vary. If you are outside the US, it is worth a quick check of your local rules.
For a clear, plain-English breakdown of the US law, the University of Minnesota Library has a reliable guide: read it here.