POSTULATES AND THEORUMS

Ruler Postulate

• the points on a line can be matched one to one with the real numbers. The real number that corresponds to the point is the coordinate for the point

• the distance between points A and B, written as AB, is the absolute value of the difference between the coordinates of A and B

Segment Addition Postulate

If A,B, and C are collinear and B is between A and C, then AB+BC=AC

Protractor Postulate

Consider line OB and a point A on one side of line OB. The rays of the form OB can be matches one to one with the real numbers from 0 to 180. The measure of angle AOB is equal to the absolute value of the different between the real numbers for line OA and line OB.

Angle Addition Postulate

If point B is the interior of angle AOC, then the measure of angle AOB + measure of angle BOC = the measure of angle AOC

Postulate 5

• a line contains AT LEAST TWO points

• a plane contains AT LEAST THREE points NOT all on one line

• space contains AT LEAST FOUR points NOT all on one line

Postulate 6

Through any TWO points there is EXACTLY ONE line

Postulate 7

Through any THREE points there is AT LEAST one plane, and through any THREE NONCOLLINEAR points there is EXACTLY ONE plane

Postulate 8

if TWO points are in a plane, then the line that contains the points is in that plane

Postulate 9

if TWO planes intersect, then their intersection is a line

Theorem 1-1

If two lines intersect, then they intersect in EXACTLY ONE point.

Theorem 1-2

Through a line and a point NOT in the line there is EXACTLY ONE plane.

Theorem 1-3

If TWO lines intersect, then EXACTLY ONE plane contains the lines.