Is there a name for a triangle which has...

Question

...such vertices (A,B,C):

• A is the origin
• B belongs to x axis
• C is anywhere (or maybe C.y > 0)

Why such a question ?

I'm looking for documentation in geometry, and a name could be an entry to begin.

NB: I'm trying to implement an algorithm to populate triangle faces of a mesh with random nodes (the blue pikes here). To generate the nodes it seems more convenient to work in 2D space. And to optimize computations it seems logic to convert the 3D triangle to a 2D triangle where the vertices are thus placed.

Answer 1

No, I think it hasn't a special name. It's simply a triangle that can be isoschele, equilater, or rectangular and so on.

Answer 2

An angle drawn that way is in standard position. I couldn't find that phrase already being used for triangles, but if I were in your shoes, I might write something like "Analogous to angles in trigonometry, we say a triangle is in 'standard position' if...".

Answer 3

I see a connection of your issue with the representation of "the space of triangles" (initiated by Kendall) like in this rich reference. where triangular shapes have one horizontal side, WLOG because the shape is independent from its orientation Of course, it is the shape itself (like if your point $B$ is constraint to be fixed, say at $(0,1)$ ; the "size" dimension has to be added afterwards or more exactly in an independent manner.