Seems like you are limiting yourself. And for NO GOOD REASON! If you can make squares and rectangles fit together properly, then that means you already know how to cut accurately, sew with a quarter inch seam, and press well.
It is not much different for triangles except you have one stretchy bias seam. There are Thangles and paper piecing and many different ways of sewing accurate triangles. I like to make a lot of half square triangles all at the same time using this method:
http://www.kathkwilts.com/lessons/halfsqr.html
Just sew slowly and don't stretch it. You will be fine!