I have been reading in multiple places (e.g. [1], section 4) that the VC-dimension of the class of triangles (in 2D space) is 7. The issue is that, for the case when 4 points lying on a straight line with alternating signs (like - + - +), I don't see why a triangle could separate the points. Where am I making mistake? [1] http://www.igi.tugraz.at/lehre/CI/SS08/tutorials/VC_examples/VC_examples.pdf 
VC-dimension of triangles in 2D space
cg.comp geom;machine learning;lg.learning;computational geometry
As Sasho and Huck mentioned in their comments, shattering means that you have to be able to separate all +/- labelings of the same set of points, given the function class. Therefore, since the set of points on a line is never separable by the class of triangles, it is not a valid set of points to decide the VC-dimension this class. 