Difference between revisions of "Triangle Angle Sum Theorem"
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| − | The '''Triangle Angle Sum Theorem''' states that for any triangle lying in the Euclidean plane that the sum of the angles is equal to <math>180^o</math> or <math> | + | The '''Triangle Angle Sum Theorem''' states that for any triangle lying in the Euclidean plane that the sum of the angles is equal to <math>180^o</math> or <math> \pi </math> 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 <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]] | ||
Latest revision as of 22:14, March 2, 2017
The Triangle Angle Sum Theorem states that for any triangle lying in the Euclidean plane that the sum of the angles is equal to <math>180^o</math> or <math> \pi </math> 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 <math> 180^o </math>.