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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

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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

reflexive property

a=a

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