Hello- Orient, Orient3pt should help, along with object snapping for precision, all of that followed by Join. This assumes your flat shapes are closed loops have been made into surfaces, (PlanarSrf command). You'll need to adjust with rotation- I suppose you can make some construction circles to help as well. I'll see if I can make an example file.
It is a little ugly- see the attached.
solid from flat triangles.3dm(133.4 KB)