Use the points to match up your next row of triangle pieces - like you show in the photo.
Clip those points that are the "inside seam" which doesn't match to anything to reduce seam bulk. For the seams that match to the strips, I would probably just clip them off to reduce bulk.
Currently I'm taking a Stack and Whack class which urges you to keep the points on to match up the seams more easily, and to clip the points on the seams that will not need to be matched.
Good luck!