Geometry was not really invented. There is a long history of the early discoveries in geometry. I will provide you with a reference. http://en.wikipedia.org/wiki/History_of_geometry
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A semi-circle
A edge in geomerty is two faces that meet.
Geomerty And Alegrba II (With trigonometry)
A line is a full 180 degrees
Geomerty is used in many ways including diagramming accidents or crime scenes, and in accident investigations.