Answer to Question #97948 in Geometry for Rachel

Question

To get a familiar sense of 'angle', look beyond the plane and the sphere, i.e., what would be an 'angle' in 3D? On the cylinder and the cone?...Does VAT apply to these broader contexts?

Answer 1

 In spherical geometry, straight lines are great circles, so any two lines meet in two points. There are also no parallel lines. The angle between two lines in spherical geometry is the angle between the planes of the corresponding great circles, and a spherical triangle is defined by its three angles. There is no concept of similar triangles in spherical geometry.

The sum of the angles of a triangle is always greater then 180°.

Vertical angles are congruent in both Euclidean and spherical geometry.