I ended up drawing squares or triangles instead. Maybe they scared me less, but he really seemed to grok it. When I asked and what's the value of "this", he'd just give the answer without knowing something about equivalent transformations and the stuff.
Made me wonder if math should maybe be taught more intuitively, not so much about the formal stuff, which in the end is pretty useless for our minds if we don't have any intuitive grasp of it.