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### 10 Cards in this Set

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• Back
 Postulate 1 The Distance Postulate: To every pair of different points there corresponds a unique positive number Postulate 2 The Ruler Postulate: The points of a line can be placed in correspondence with the real numbers in such a way that (1) to every point of the line there corresponds exactly one real number (2) to every real number there corresponds exactly one point of the line (3) the distance between any two points is the absolute value of the difference of the corresponding numbers Postulate 3 The ruler Placement postulate. Given two points P and Q of a line, the coordinate system can be chosen in such a way that the coordinate of P is zero and the coordinate of Q is posituve Postulate 4 The Line Postulate: For every two points there is exactly one line that contains both points Postulate 5 The Plane-Space Postulate: (a) Every plane contains at least three noncollinear points (b) Space contains at least four noncoplaner points Postulate 6 The Flat Plane Postulate: If two points of a line lie in a plane, then the lies in the same plane Postulate 7 The Plane Postulate: Any three points lie in at least one plane ,and any three noncollinear points lie in exactly one plane Postulate 8 Intersection of Planes postulate If two different planes intersect, then their intersection is a line Postulate 9 The plane Separation Postulate Given a line and a plane containing it, the points of the plane that o not lie on the line form two sets such that (1) each of the sets is convex, and (2) if P is in one of the sets and Q is in the other, then the segment PQ intersects the line Postulate 10 The Space Separation Postulate: The points of space that do not lie in a given plane form two sets such that: (1) each of the sets is convex, and (2) if P is in one of the sets and Q is in the other, then the segment PQ intersects the plane