How do you deal with rumors in high school?

It's none of your business! Keep calm and just ignore them. Rumours are made in order to angry people. If you keep acting patiently, people won't believe it. Because there's nothing interesting.

ignore them but let your close friends know they are not true

If you are a decent person, keep acting as usual, let others see you all the time spending your time on decent conversations, in the library, talking to teachers and such.