Triangle Angle Sum Theorem

The Triangle Angle Sum Theorem states that for any triangle lying in the Euclidean plane that the sum of the angles is equal to or radians.

This is one of the facts that characterizes Euclidean geometry: it is not, however, true in other geometries. The proof for this theorem is reliant on the parallel postulate, so does not generalize into other geometries. For example, any triangle constructed on the surface of the earth (known as a spherical triangle) the sum of the angles is always greater than .