As the size of triangles increases, on Earth's surface, the sum of the three angles exceeds 180 degrees (with modern instruments, this is easy to detect). The amount of spherical excess is directly proportional to the area covered by the triangle, relative to the total area of the sphere. This is only possible on a finite, positively curved surface.
"Flat" triangles do not have spherical excess.
Even this was already understood by Greek geometers, over 2000 years ago.