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Definition


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Definition
If a = b + c and c > 0, the a > b 


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Definition
To every pair of different points there corresponds a unique positive number 


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Definition
The points of a line can be placed in corespondence with the real numbers in such a way 1. to every point 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 


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Postulate 3  Ruler Placement 

Definition
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 positive. 


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Definition
Let a,b, and c be points of a line, with coordinates x,y, and z repectively. If x 


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Definition
If a,b, and c are three different points of the same line, then exactly one of them is between the other two. 


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Definition
For every two different points there is exactly one line that contains both points. 


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Definition
Let AB be a ray, and let x be a positive number, THen there is exacltly one point of P of ray AB such that AP = x. 


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Definition
Every segment has exactly one midpoint 


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Definition
If two different line intersect, their intersection contains only one point. 


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Postulate 5  Plainspace 

Definition
a every plane contains at least three different noncollinear points. b space contains at least four different noncoplanar points. 


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Definition
IF two points of a line lie in a plane, then the line lies in the same plane. 


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Definition
IF a line intersects a plane not containing it, then the intersection contains only one point 


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Definition
Any three points lie in at least one plane, and any three noncollinear points lie in exactly one plane. 


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Definition
Given a line and a point not on the line, there is exactly one plane containing both. 


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Definition
Given two intersecting line, there is exactly one plain containng both. 


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Postulate 8 Intesection of Planes 

Definition
IF two planes intersect, then their intersection is a line 


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Poatulate 9 Plane separation 

Definition
GIven a line and a plane containing it. THe ponts of a plane that do not lie on the line form two sets sich that 1. each of teh sets is convex 2. id p is in one of the sets and q is in the other, the the segment pq intersects the line 


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Postulate 10 Space separation 

Definition
THe points of space that not lie in a a given plane form two sets such that 1. each of the sets is convex 2. if p is one of the sets and q is in the other, then the segents pq intersects the plane. 

