Hi Dent,
If you add a construction plane using 3 points, you can then sketch on that plane. I think you have all the points you need.
My approach to creating your “golden rectangle pyramid!?!” is to create one right triangle and rotate it along the long leg. By copying and rotating twice at 120 degrees, you build a “frame”. Then you can add construction planes using the 3 point method to define the faces of the pyramid.
I did something like that, then made a triangular prism body and used the planes to split that body.
