We prove that, in ordered plane geometries endowed with a very weak notion of orthogonality, one can always triangulate any triangle into seven acute triangles, and, in case the given triangle is not acute, into no fewer than seven.

MSC Classifications:

51G05, 51F20, 51F05 show english descriptions Ordered geometries (ordered incidence structures, etc.)
Congruence and orthogonality [See also 20H05]
Absolute planes 51G05 - Ordered geometries (ordered incidence structures, etc.)
51F20 - Congruence and orthogonality [See also 20H05]
51F05 - Absolute planes

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