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Postulates and Theorems of Geometry

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Postulate 1: Ruler Postulate
The points on aline can be matched one to one with the real numbers. The real number that corresponds to a point in the coordinate of the point. This distance between points A and B, written as AB, is the absolute vallue of the difference between A and B.
Postulate 2: Segment Addition Postulate
If B is between A and C, then AB+BC=Ac. If AB+BC=Ac, the B is between A and B.
Postulate 3: Protractor Postulate
Consider point A on one side of lineOB. THe rays of the form rayOA can be matched one ot one with the real numbers from 0 to 180. THe measure of angleAOB is equal to the absolute value of the difference between the real numbers for rayOA and rayOB.
Postulate 4: Angle Addition Postulate
If P is in the interior of angleRST, then m-angleRSP+m-anglePST=m-angleRST.
Postulate 5:
Through any two points, there exists exactly one line.
Postulate 6:
A line contains atleast 2 points.
Postulate 7:
If 2 lines intersect, then their intersection is exactly one point.
Postulate 8:
Through any 3 noncollinear points, there exists exactly one plane.
Postulate 9:
A plane contains atleast 3 noncollinear points.
Postulate 10:
If two points lie on a plane, then the line containing them lies in the plane.
Postulate 11:
The intersection of two planes is exactly one line.
Postulate 12: Linear Pair Postulate
If two angle sform a linear pair, then they are supplementary.
Postulate 13: Parallel Postulate
If there is a line and a point not on the line, then there is exactly one line through the point that is parallel to the given line.
Postulate 14: Perpendicular Postulate
If there is a line and a point not on the line, then there is exactly one line through the point that is perpendicular to the given line.

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