C172 CFI reported a NMAC with a helicopter while scanning for other known traffic. Instructor took controls from student and made a sharp turn to avoid helicopter.

Narrative

I was the instructor on a routine training flight departing from ZZZ around XA15. Our aircraft was not equipped with ADS-B in capabilities or traffic awareness systems. The flight was a training flight for the student's instrument rating; so the student was wearing a view-limiting device. We departed the pattern and turned towards the Southeast; climbing up to 3500 MSL. There was a moderate amount of haze to the SE; which did somewhat limit visibility. Once we reached our cruising altitude; another Cessna 172 from the same flight school called the CTAF informing that they were maneuvering near our current position and would be climbing through our current altitude. Knowing that they would be off our right wing; I began scanning the area to the right; searching for the traffic. After looking for about 20 seconds; I turned to look out the front of the plane; only to see a helicopter at our same altitude (3500msl) less than half a mile in front of us flying NW-bound towards us. Due to the helicopter's bearing towards us; I determined the best course of action would be to enter a sharp turn to the left; which I promptly did; taking the controls from my student. The pilot of the helicopter did the same a moment later. No radio calls were heard from the medical helicopter before; during; or after the incident. At this time my student and I elected to discontinue the flight and return to ZZZ.