Geometry Postulates And Theorems

Front 1

Postulate 1: Ruler Postulate

Back 1

- the points on a line can be paired with the real numbers in such a way that any two points can have coordinates 0 and 1
- once a coordinate system has been chosen in this way, the distance between any two points equals the absolute value of the difference of their coordinates

Front 2

Postulate 2: Segment Addition Postulate

Back 2

- If B is between A and then C then; AB + BC = AC

Front 3

Postulate 3: Protractor Postulate

Back 3

-On line AB in a given plane, choose any point O between A and B. Consider ray OA and ray OB and all the rays that can be draw from O on one side of line AB. These rays can be paired with the real numbers from 0 to 180 in such a way that:
-Ray OA is paired with 0 and ray OB with 180
-If ray OP is paired with x and ray OQ with y then the measure of angle POQ equals the absolute value of x – y

Front 4

Postulate 4: Angle Additon Postulate

Back 4

- if point B lies in the interior of angle AOC then the measure of angle AOB plus the measure of angle BOC equals the measure of angle AOC. If angle AOC is a straight angle and B is any point not on Line AC then the measure of angle AOB and the measure of angle BOC equals 180

Front 5

Postulate 5

Back 5

-a line contains at least two points; a plane contains at least three points not all in one line; space contains at least four points not all in on plane

Front 6

Postulate 6

Back 6

- through any two points there is exactly one line

Front 7

Postulate 7

Back 7

- through any three points there is at least one plan and through any three noncollinear points there is exactly one plane

Front 8

Postulate 8

Back 8

- if two points are in a plane then the line that contains the points is in that plane

Front 9

Postulate 9

Back 9

- if two planes interesect then their intersection is a line

Front 10

Theorem 1-1

Back 10

- if two lines interesect then they interset in exactly one point

Front 11

Theorem 1-2

Back 11

- through a line and a point not in the line there is exactly one plane

Front 12

Theorem 1-3

Back 12

- f two lines interesect, then exactly one plane contains the lines