Student pilot reported a conflict with a seaplane that was departing from a lake located below the GIF traffic pattern.

Narrative

During downwind flight within the traffic pattern for Runway 05; a seaplane took off below us into the left downwind portion of the traffic pattern at a non-towered airport; GIF. My instructor took the controls and turned the plane so that I could see the plane departing beneath us and then I resumed controls for the remainder of the flight when I had the traffic in sight. There is a lake on the southwest corner of the airport where the seaplane departed; but as this was the first time at this airport; my instructor and I were unaware.I made radio calls entering and throughout the traffic pattern and heard nothing from the seaplane. I realize the seaplane was not required to have / utilize a radio. However; this seemed to represent an unnecessary hazard considering the location of the lake used for seaplane departures and landings. I write this in the hope that seaplanes no longer be allowed to take off under a traffic pattern of a non-towered airport when the use of radios are not required. A final note; my instructor departed the airport without me and told me of other dangerous activities within the traffic pattern of the seemingly busy airport and expressed concern of the safety should we ever decide to fly into that airport again in the future.