Exterior Angle Inequality Spherical Geometry
Exterior Angle Inequality
The Exterior Angle Inequality says that the measure of an exterior angle of a triangle is greater than the measure of each of its remote interior angles.
This theorem is FALSE in Spherical Geometry.
However, if we restrict the lengths of the sides of the triangles to be less than pi/2, then the theorem is true for Spherical Geometry. (u = pi above).
The theorem is true in Euclidean and Hyperbolic Geometries without any restriction.