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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 [[Non-Euclidean geometry|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 <math> 180^o </math>.
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 [[Non-Euclidean geometry|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 <math> 180^o </math>.
[[Category:Plane Geometry]]
[[Category:Plane Geometry]]
[[Category:Geometric Theorems]]