Honors Geometry Lesson Three Postulates and Theorems

postulate

postulate

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