Relating Points, Lines, and Relating Points, Lines, and PlanesPlanes

Key wordsKey words

THEOREMS:THEOREMS: statements that statements that

cancan be proved. be proved.

POSTULATE:POSTULATE: statements that statements that

cannotcannot be proved. be proved.

So what?So what?

Just like Geometry started with three Just like Geometry started with three undefined terms (what are they?), it undefined terms (what are they?), it also had to start with five “unproved” also had to start with five “unproved” postulates.postulates.

From these five postulates come all From these five postulates come all geometric theorems.geometric theorems.

They are the foundation for Geometry!They are the foundation for Geometry!

Postulate 5Postulate 5

A line contains at least A line contains at least two points; two points;

a plane contains at least a plane contains at least three points; three points;

space contains at least space contains at least four points not all in one four points not all in one plane.plane.

Postulate 6Postulate 6

Through any two points Through any two points there is exactly one line.there is exactly one line.

Postulate 7Postulate 7

Through any three points Through any three points there is at least one plane, there is at least one plane, and through any three and through any three noncollinear points there noncollinear points there is exactly one plane.is exactly one plane.

Postulate 8Postulate 8

If two points are in a If two points are in a plane, then the line that plane, then the line that contains the points is in contains the points is in that plane.that plane.

Postulate 9Postulate 9

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

Now its time for the Now its time for the

THEOREMSTHEOREMS!!!!!!!!!!

Theorem 1-1Theorem 1-1

If two lines intersect, If two lines intersect, then they intersect in then they intersect in exactly one point.exactly one point.

Theorem 1-2Theorem 1-2

Through a line and a point Through a line and a point not in the line there is not in the line there is exactly one plane.exactly one plane.

Theorem 1-3Theorem 1-3If two lines intersect, If two lines intersect, then exactly one plane then exactly one plane contains the lines.contains the lines.

PRACTICEPRACTICE

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