I don't draw a line, I line up the corner with the line on my template attached to the machine bed.
When I'm going scrappy, I normally use my Easy angle to cut my triangles, I do not cut squares and then cut in half. I have absolutely no problem dealing with bias edges. I think it's because I had 30 years of garment construction under my belt before starting to make quilts. Quilting cotton fabric is about the easiest thing I can think of to sew.