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Is the triangle angle sum theorem true on the surface of a sphere?
2 Answers
- TomVLv 76 months agoFavorite 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°.
