I taught Geometry this spring, and we spent about half the semester working through Euclid (Book I and a smattering of some others). We proved SAS (Side Angle Side), ASA, AAS, but not ASS (Angle Side Side). Because there is no ASS in Geometry.
Here <A=<A’, AB=A’B’, and BC=B’C’ but the two triangles are not congruent. All we get are bad jokes.
Except that’s not quite true! If <A=<A’, AB=A’B’, BC=B’C’, and BC≥AB, then the two triangles are congruent! In class, I referred to this theorem as ASS.
(The Hypotenuse-Leg Theorem is a special case of this, since the hypotenuses, as the sides across from the corresponding right angles, are certainly longer than the corresponding legs of the triangle).
We didn’t refer to this theorem very often, but it is, well, memorable. And so Adele, one of our majors, was thrilled when she noticed ASS written on a van this past weekend! She snuck a photo of it:
According to Adele and everyone who was with her, this is exactly how I would write the shorthand. We have no idea why it’s on this van. I like to think that this is a Secret Geometry Van, coming out to help students everywhere by providing them with extra theorems.