POINT LINE AND PLANE POSTULATES

Postulate 1 : 

Through any two points, there exists exactly one line. 

Postulate 2 : 

A line contains at least two points. 

Postulate 3 : 

If two lines intersect, then their intersection is exactly one point. 

Postulate 4 : 

Through any three noncollinear points, there exists exactly one plane. 

Postulate 5 : 

A plane contains at least three noncollinear points. 

Postulate 6 : 

If two points lie in a plane, then the line containing them lies in the plane. 

Postulate 7 : 

If two planes intersect, then their intersection is a line. 

Example

Use the diagram shown below to give examples of postulates 1 through 7.

Solution : 

Postulate 1 : 

There is exactly one line (line n) that passes through the points A and B. 

Postulate 2 : 

Line n contains at least two points. For instance, line n contains the points A and B. 

Postulate 3 : 

Lines m and n intersect at point A. 

Postulate 4 : 

Plane P passes through the noncollinear points A, B and C. 

Postulate 5 : 

Plane P contains at least three noncollinear points A, B and C. 

Postulate 6 : 

Points A and B lie in plane P. So, line n, which contains points A and B, also lies in plane B.    

Postulate 7 : 

Planes P and Q intersect. So, they intersect in a line, labeled in the diagram as line m.    

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