You don't have to do a Y seam, but you will have to do a partial seam.
With the pink triangles, sew each one on half way (does not have to be an 'exact' stopping point.) Do all four pink triangles like this.
Now go back to any triangle. Lift up the edge that is unsewn, lay the rectangle strip down under it along the focus fabric, and sew that rectangle down along the focus fabric and along the edge of your triangle. Then you will just have to finish the triangle seams where you stopped.