So far, in different articles and books the concepts of modern definition of geometry and Minkowskian, Galilean planes and spaces have been introduced. In this paper, we are going to describe geometry that is improved by W. Thurston and then we are going to introduce you to geometries that are suitable to this description in 2 dimensional planes.
The main difference of Galilean geometry is its relative simplicity, for it enables the student to study it in relative detail without losing a great deal of time and intellectual energy. In this paper, we introduce you with new geometric(non-Euclidean) ideas which exist in affine plane and more simple than Euclidean plane.
In this paper, we have tried to indicate the own properties of polygons in Galilean geometry using the Affine concepts as well. The relationships between an angle and a side as well as the relationships between altitudes and medians concepts, and comparison of some special polygons have been examined carefully. In addition, the area concept has been mentioned. Finally, the paper was completed with a new idea, Theorem 6.
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