###
Ruler Postulate

the points on a line can be paired with all real numbers and the distance on the line is found by taking the absolute value of the difference of their coordinates.

###
Segment Addition Postulate

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

###
Protractor Postulate

Given a strait angle rays can be paired with numbers from 0 to 180. the measure of an angle is the absolute value of the difference of the numbers paired with rays.

###
Angle Addition Postulate

If P is in the interior of RST, then mRST=mRSP+mPST

###
Post. 5

A line contains at least 2 points, a plane at least 3 non collinear points, and space at least 4 non coplanar points.

###
Line postulate

Through any two points there exists exactly one line.

###
plane postulate

7, Any 3 points are contained in at least one plane, and 3 non-collinear points determine a plane.

###
flat plane postulate

if two points lie in a plane, then the line containing those points lies in the plane

###
plane intersection postulate

9, if two planes intersect, then their intersection is a line

###
addition property

, if a=b and c=d, then a+c=b+d

###
subtraction property

If a=b and c=d, then a-c=b-d

###
multiplication property

If a=b, then ac=bc

###
division property

if a=b and c≠0, then a/c=b/c

###
substitution property

if a = b, then a can be substituted for b in any equation or expression

###
symmetric property

If a=b, then b=a

###
transitive property

If a=b and b=c, then a=c

###
distributive property

a(b+c)=ab+ac

###
line intersection theorem

2 different lines intersect in at most ONE POINT

###
plane determination theorem

Through a line and a point not on a line, there is exactly one plane.

###
midpoint theorem

if M is the midpoint of segment AB, then AM=1/2AB and MB=1/2AB

###
Angle Bisector theorem

If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle

###
supplementary theorem

If two angles for a linear pair, then they are supplementary angles

###
verticle angle theorem

If two angles are vetical angles, then they have equal measures

###
2-4 theorem

perpendicular lines form congruent adjacent angles.

###
2-5 theorem

if 2 lines for congruent adjacent angles then they are perpendicular.

###
2-6

if the outside rays of two adjacent acute angles are perpendiculalr, then the angles are complementary.

###
supplements of congruent angles theorem

supplements of congruent angles are congruent

###
compliments of congruent angles theorem

compliments of congruent angles are congruent

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