Studied by 2 peoplepostulate
a statement that is accepted as true without proof
theorem
a statement that can be proven (through a proof)
Three Characteristics of A Postulate
consistent (they do not contradict each other), independent, complete
incident postulates
expansion postulate, line postulate, plane postulate, flat postulate, line intersect postulate, plane intersection, and postulate (entire structure of Geometry is built on these postulates)
expansion postulate
A line contains at least two points. A plane contains at least three noncollinear points. Space contains at least four noncoplanar points.
Line Postulate
only two points in space lie on exactly one line
Flat Postulate
If two points are in a plane, then the line that contains them is also in that plane
Line Intersect Postulate
If two lines intersect, then their intersection is exactly one point
Plane Intersection Postulate
If two planes intersect, then their intersection is exactly one line.
Theorem 1.3.2
two intersecting lines are contained in one and only one plane
Theorem 1.3.3
Two parallel lines are contained in one and only one plane.
theorem 1.3.1
A line and a point not on that line are contained in one and only one plane.
Plane Postulate
any three noncollinear points lie in exactly one plane
Ruler Postulate
every point on a line can be placed in one-to-one correspondence with a real number
Note
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