Take any three points on earth with a significant distance apart (Paris, London, and Berlin, for instance) and you will find the angles add up to greater than 180 degrees. This is called positive curvature and implies the Earth is round (or at least curved in the area measured). If the angles do add up to 180 degrees as they do in plain-old Euclidean geometry then you have a flat surface. Triangles whose angles measure less than 180 degrees imply a negative curvature (like a horse saddle).