I have this shape:
,
and I want to put a straight line somewhere through the shape to cut it into two triangles. I know that this is possible, but I don't know how. Any help is appreciated!
2026-04-01 07:00:01.1775026801
Cut A Shape Into Two Triangles
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Adding a line segment, there are three exhaustive, mutually exclusive cases:
Case $1$: Both endpoints of the line segment lie on a side of the original shape.
Case $2$: One endpoint of the line segment lies on a vertex, and the other endpoint lies on a side.
Case $3$: Both endpoints of the line segment lie on a vertex of the original shape.
If you can split this figure into two triangles with a single line segment, the resulting two triangles must share a side and have $4$ vertices between them (without double-counting). Given these cases, is this ever possible?
Another way to think about it:
You can think about the problem as bringing two triangles together, and those two triangles must share a side (which is the line segment you draw). Bringing any two triangles together in such a way results in a larger shape that has $4$ vertices, but the original shape here has $5$.