C172 instructor reports NMAC with PA28 during night visual approach from the traffic pattern. PA28 pilot; who is below and behind; and does not make a base turn call. Another C172 pilot makes 360 degree turn on final to avoid the PA28.

Narrative

I was flying with my student in the traffic pattern at ZZZ. We were on base for Runway XX about to turn final when another airplane turned final 200 FT behind us. We did not recognize the traffic prior to the incident. There was a second C172 on a long final about 3 NM doing the GPS 11 approach. We had visual contact with them and we also talked to each other to clarify our intentions. Suddenly we heard a person swearing over the radio; 'You just cut me off!' We do not know who the person was. After landing; we saw a PA28 landing right after us. And still a person swearing over radio at us. I said we can discuss the situation after I finished my flight lesson and we can meet at the airport. At this time it was not clear where the airplane came from and who the pilot was. We assumed first it was the C172 on the instrument approach; whom I personally know. Later that evening I spoke to the crew of the C172 to clarify the incident. He stated that there was a third plane; a PA28; on final who forced them to make 360 degree turn and they saw that this airplane was 200 FT behind and 100 FT low and turned at the same time on final like we did. The pilot of the PA28 was a local pilot who also flew in the traffic pattern which he overextended and he also did not follow the exact radio procedures. We did not see the PA28 until it landed. After the end of the flight; my student and I prepared our plane to put in the hangar when PA28 pilot came over and verbally and physically assaulted me.