Introduction to Modern Geometry Modern Geometry: The Directed Line Segment In Euclidean Geometry, line segments possess only magnitude, and not direction. A B Figure 1: In Euclidean Geometry, only the magnitude of line segments is considered. As we can see in Figure 1 , in Euclidean Geometry, the line segment: |AB| would be considered equal to the line segment: |BA| . However, this is not the case with Modern Geometry. In Modern Geometry, line segments not only possess magnitude, but direction also. A B Figure 2: In Modern Geometry, line segments possess direction as well as magnitude. In Modern Geometry: |AB| is termed: ‘a directed line segment’ . ...
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