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10 Cards in this Set

  • Front
  • 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