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CHAPTER TWO LINE REFLECTIONS
CHAPTER NINE LENGTH AND DISTANCE
According affine plane affinity algebraic assigns axioms base choose circle collinear common complex number composition congruent consider contains coordinate system COROLLARY defined DEFINITION derive determines direction distance distance preserving transformation distinct points elements end points equal equation Euclidean plane exactly EXERCISES expression fact field Figure fixed points follows formal formulas function geometry given h-congruent h-line h-points h-ray h-triangle infer interpretation intersection introduce inversion isometry LEMMA length length function line reflection linear mathematical measure obtain Ol coordinate ordinary origin pair parallel projection perpendicular plane positive Proof Prove real numbers relation relative respective result satisfy segment sends sensed angles set of points side solution Suppose tangent THEOREM unique vertex vertices whence x-axis