"Broken" on purpose -- tranchet flaked to produce a burin (chisel) edge. One straight across and the other north-south. Not seen that often seen in North America although very common in Europe.
Accidental snapping from strenuous use would have produced a rolled-over hinge surface; no usual (typical) use after (or before) that could have created the vertical tranchet removal. At the same time, one would set up the other, no matter which sequence was the case.
Interesting, the reason I asked is because I find pottery that is identical over here in se Kansas in a particular site but I find a lot of small points there, nothing substantial like your points. To me, the way the base of the second is formed, I suspect that it was once a much larger point too.