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Postulates -Theorems

Geometry postulates and theorems

Postulate 5 Through any two points there exists exactly one line
Postulate 6 Through any three noncollinear points there exists exactly one plane
Theorem 4-1 If two lines intersect, then they intersect at exactly one point
Theorem 4-2 If there is a line and a point not on the line, then exactly one plane contains them
Theorem 4-3 If two lines intersect, then there exists exactly one plane that contains them
Postulate 7 If two planes intersect, then their intersection is a line.
Postulate 8 If two points lie on a plane, then the line containing them lies in the plane
Postulate 9 A line contains at least 2 points. A plane contains at least three noncollinear points. Space contains at least 4 noncoplanar points
Theorem 5-2 If two lines in a plane are perpendicular to the same line, then they are parallel to each other
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.
Theorem 5-1 If two parallel planes are intersected by a third plane,then the lines of intersection are parallel
Theorem 5-4 If two lines are perpendicular, then they form congruent adjacent angles
Theorem 5-5 If two lines form congruent adjacent angles, then they are perpendicular
Theorem 5-6 All right angles are congruent
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
Theorem 5-7: Transitive Property of Parallel Lines If two lines are parallel to the same line, then they are parallel to one another
Created by: ojw1230