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Geometry Theorems and Postulates
lkkljlk
20
Mathematics
09/30/2012

Term
 Theorem 2-1
Definition
 If a - b > 0, then a > b
Term
 Theorem 2-2
Definition
 If a = b + c and c > 0, the a > b
Term
 Postulate 1 - Distance
Definition
 To every pair of different points there corresponds a unique positive number
Term
 Posulate 2 - Ruler
Definition
 The points of a line can be placed in corespondence with the real numbers in such a way1. to every point there corresponds exactly one real number2. to every real number there corresponds exactly one point of the line3. the distance between any two points is the absolute value of the difference of the corresponding numbers
Term
 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.
Term
 Theorem 2-3
Definition
 Let a,b, and c be points of a line, with coordinates x,y, and z repectively. If x
Term
 Theorem 2-4
Definition
 If a,b, and c are three different points of the same line, then exactly one of them is between the other two.
Term
 Postulate 4 - LIne
Definition
 For every two different points there is exactly one line that contains both points.
Term
 Theorem 2-5
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.
Term
 Theorem 2-6
Definition
 Every segment has exactly one midpoint
Term
 Theorem 3-1
Definition
 If two different line intersect, their intersection contains only one point.
Term
 Postulate 5 - Plain-space
Definition
 a- every plane contains at least three different noncollinear points.b- space contains at least four different noncoplanar points.
Term
 Posulate 6- Flat Plane
Definition
 IF two points of a line lie in a plane, then the line lies in the same plane.
Term
 Theorem 3-2
Definition
 IF a line intersects a plane not containing it, then the intersection contains only one point
Term
 Postulate 7- Plane
Definition
 Any three points lie in at least one plane, and any three noncollinear points lie in exactly one plane.
Term
 Theorem 3-3
Definition
 Given a line and a point not on the line, there is exactly one plane containing both.
Term
 Theorem 3-4
Definition
 Given two intersecting line, there is exactly one plain containng both.
Term
 Postulate 8- Intesection of Planes
Definition
 IF two planes intersect, then their intersection is a line
Term
 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 that1. each of teh sets is convex2. id p is in one of the sets and q is in the other, the the segment pq intersects the line
Term
 Postulate 10- Space separation
Definition
 THe points of space that not lie in a a given plane form two sets such that1. each of the sets is convex2. if p is one of the sets and q is in the other, then the segents pq intersects the plane.
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