Flight Instructor reported an NMAC with another light aircraft in the pattern at ZZZ airport.

Narrative

During a part 91 VFR day flight; I was conducting a training flight as a flight instructor in accordance with my school's part 141 training curriculum. I was sitting in the left seat of Aircraft X as my student; a flight instructor applicant with a commercial certificate ASEL; was the manipulator of the controls for this flight sitting in the right seat. We departed ZZZ from runway XX in VFR conditions; to the southeast of the airport approximately 10NM for VFR maneuvers. After about 45 minutes of various maneuvers; we intended to return to the traffic pattern to do about 2 to 3 laps in the pattern. I had an IPAD EFB in my lap with software the was connected to the aircraft's GPS with dedicated ADS-B in/out capability for extra situational awareness as per my usual personal procedure due the extremely high volume of traffic in the area. The runway we departed from; was also the runway of intended landing. For a morning it was very quiet on the CTAF and I observed no aircraft in the traffic pattern; or in the areas surrounding the airport visually or on ADS-B. Per my school's SOP and per FAA guidance we entered the traffic pattern at pattern altitude with a 45 degree entry. We arrived in the traffic pattern and conducted a stop and go landing on runway 17. We proceeded to depart again for another lap in the pattern making a crosswind turn at approximately 1500 ft MSL. My student was making the appropriate traffic calls on frequency and announced we were Turing left downwind for runway XX. We turned downwind at 1700 MSL and as we rolled our wings level from downwind; I looked to my 2 o'clock position and observed an aircraft at the same altitude and approximately 50 ft or less laterally. We were in conflict and from my experience I knew a collision was imminent. Due to the close proximity we were unable to take any evasive action to adequately avoid a collision. Both of our aircraft did not manage to collide and I announced that I was taking the controls and maneuvered the aircraft from the intruder who was in front of us now less than a 1/4NM. I offset to the right to keep Aircraft Y in sight. He commenced a descent in the downwind as we were in trail. He was not making any radio calls on CTAF and we did not observe him on the aircraft's ADS-B nor my EFB. I queried on CTAF to confront the other pilot to see if had me in sight; and of his intentions. I received no response and we were still in trail of Aircraft Y as be made is base and final turns with his landing where I observed him vacate the runway and taxi to the FBO after announcing on CTAF that he was clear of the runway. During my turn from downwind to crosswind my visual scan outside the airplane was to the 45 degree downwind looking for aircraft entering the pattern. We did not observe any aircraft on the 45 or downwind. We came close to a collision and in my experience of over 1500 flight hours at my airports uncontrolled operation; I've seen these instances of close calls and near misses increase substantially in the previous 2 years. I'm confident with the growing number of traffic and people not adhering to recommended pattern entry guidance that these instances of close calls and near misses will continue; if not increase.