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Geometry postulates and theorems

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Question
Answer
Postulate 5   Through any two points there exists exactly one line  
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Postulate 6   Through any three noncollinear points there exists exactly one plane  
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Theorem 4-1   If two lines intersect, then they intersect at exactly one point  
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Theorem 4-2   If there is a line and a point not on the line, then exactly one plane contains them  
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Theorem 4-3   If two lines intersect, then there exists exactly one plane that contains them  
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Postulate 7   If two planes intersect, then their intersection is a line.  
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Postulate 8   If two points lie on a plane, then the line containing them lies in the plane  
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Postulate 9   A line contains at least 2 points. A plane contains at least three noncollinear points. Space contains at least 4 noncoplanar points  
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Theorem 5-2   If two lines in a plane are perpendicular to the same line, then they are parallel to each other  
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Theorem 5-3   In a plane, if a line is perpendicular to one of two parallel lines, then it is perpendicular to the other one.  
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Theorem 5-1   If two parallel planes are intersected by a third plane,then the lines of intersection are parallel  
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Theorem 5-4   If two lines are perpendicular, then they form congruent adjacent angles  
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Theorem 5-5   If two lines form congruent adjacent angles, then they are perpendicular  
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Theorem 5-6   All right angles are congruent  
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Postulate 10: The Parallel Postulate   Through a point not on a line, there exists exactly one line through the point that is parallel to the line  
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Theorem 5-7: Transitive Property of Parallel Lines   If two lines are parallel to the same line, then they are parallel to one another  
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