I tried to be all witty and make my triangle vertices have the "love" theme.
I had ΔSWT and ΔHUN, ΔHRT. I feel I have to mention what I was going for: "sweet", "hun" as in "honey", and "heart". As I was walking around the room and a student asked me about the names, another pipes up, "oh! I thought that was SWT for Swastika or Swat and HUN like Attila the Hun and HRT like Hurt".
Then a student was having trouble remembering which triangles gave the ambiguous case. So I pulled out my handy-dandy spaghetti and cut some angles out of construction paper:
And I started snapping off spaghetti and walking through SAS and ASA and such asking, "if you were given this information and it was fixed, could you make one or more than one triangle?" ... It was fast and I think effective.