On bearisgray's drawings, you can see that the triangle piece does not need the tip. If you laid your template/pattern on a strip, it would not need to be wider than the other strips, and you cut the triangles with no tips. That gets cut off anyhow.
Sewing with those tips gone makes it much easier to line up the pieces. I did triangles with strips around, and found it was much easier after all the tips were gone.




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