The problem discussed above (my humble explanation) is that SU native system lacks a true compass-like function--in order to do some basic geometric manipulation. And since circles are only made of segments, they don't help. If you try to rotate to intersect a line you can't accurately do it, unless you already have a point right where it should intersect. The plugins can do it.
Or did Dave figure out a way? I fooled with it and couldn't.
I don't think it has anything to do with the behavior of triangles. When you move a point in Sketchup, it just moves and stretches edges however it needs to. That seems intuitive to me. So grouping (by making a group or a component) means the edges and endpoints cannot move independently and a triangle or any form holds its shape unless you edit the group (by double clicking) (OK, not entirely true- you can scale the component non-uninformly). The reason you probably saw a difference in rectangles is because SU will tend to resist deforming a face by creating more faces (unless you push the right buttons, e.g. up-arrow). SU will lock movement to be within the plane as a default; and this can be helpful in some situations--like boxy architecture SU was designed for 😉 .