 In the Euclidean case, equality occurs only if the triangle has a angle and two angles, making the three vertices collinear, as shown in the bottom example.Thus, in Euclidean geometry, the shortest distance between two points is a straight line.In spherical geometry, the shortest distance between two points is an arc of a great circle, but the triangle inequality holds provided the restriction is made that the distance between two points on a sphere is the length of a minor spherical line segment (that is, one with central angle in ) with those endpoints.