When explaining planes, I ask the class if anyone has ever sat in a wobbly chair and challenged them to explain why it wobbled. They will usually say that it was because one of the legs was “messed up.” At this point I’ll pick up a “non-wobbly” chair in the room and show them that the reason it isn’t wobbly is because all the points touch the ground at the same time, hence they are coplanar. I’ll even place the chair to the ceiling showing that they all touch the ceiling at the same time. But the moment one of the caps comes off on one of the legs, it is no longer coplanar with the other three legs, creating the wobble.
I then go into why cameramen always use tripods to keep the camera steady. Three legs will always be planar, but not four.