Is the triangle angle sum theorem true on the surface of a sphere?

?2020-10-15T14:55:59Z

Favorite Answer

No.
The sum of the angles of a triangle is equal to 180° only in Euclidian or Plane Geometry. The sum of the angles of a triangle on the surface of a sphere is greater than 180°.

Consider the case of 2 meridians that intersect at a pole. Those meridians intersect the equator with base angles of 90° and each other at an apex angle between 0 and 360­°. The two meridians and the equator form the three sides of a spherical triangle. The sum of the angles is obviously greater than 180°. 

billrussell422020-10-15T16:01:18Z

no