In third grade, they drew rays and they had to name them. (I thought, name it like AB or something, from the points on the ray).
My son labeled one "David" and another "Tony." He said those were his best friends' names!
I thought he was goofing around but that was what the Everyday Math publishers wanted- a way for children to "get comfortable" with math!!
That is too funny!

I would definitely have tried to shut down that approach, with exactly the thought that you were having! I can see that discussion with DD now. "No, honey, you can't name them Gavin and Ty." "But teacher said so!"
Well, about the triangle -- I'm glad it's not just me. I thought I was missing something really stupid, there. I'll have to ask the teacher exactly what it was they were looking for.
It was made more complicated by the fact that I couldn't find a compass and had to make one from a pair of scissors. I thought about cutting out a circle the right size, instead, but I didn't want to make it seem that much more difficult for DD.