Single engine Instructor reported a NMAC while turning base at a non-towered airport. The Instructor said a helicopter proceeded straight in; cutting the Instructor off; hoovering over numbers and then departing straight out. No communication from the helicopter.

Narrative

During a training session in traffic pattern with my student; while descending and turning base to final; making position announcements on CTAF and scanning for unannounced traffic; we saw a helicopter that was rapidly approaching on a straight-in final that we previously didn't see and that wasn't in the pattern; cutting us off and dropping over the runway numbers and hovering. Immediately I took over the controls from my student and had to make an evasive maneuver to avoid a possible collision. I made a 360 degrees right turn with a steep climb to avoid the helicopter that after hovering; started a vertical climb and immediately left the airport on straight out departure. I tried to communicate with the helicopter and received no response on CTAF. Without having situational awareness and being cautious while training in an uncontrolled airport; situation could've been much worse.After landing safely; I emphasized to my student the importance of making CTAF position announcements; scan for traffic; and always enter the traffic pattern on the recommended FAA procedures and per the new recommendations of AC 90-66C. 'If you don't see them or hear them; doesn't mean they're not there!'