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.