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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.

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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.

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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.

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Angle Addition Postulate

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

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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.

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Line postulate

Through any two points there exists exactly one line.

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plane postulate

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

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flat plane postulate

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

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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

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subtraction property

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

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multiplication property

If a=b, then ac=bc

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division property

if a=b and c≠0, then a/c=b/c

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substitution property

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

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symmetric property

If a=b, then b=a

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transitive property

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

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distributive property

a(b+c)=ab+ac

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line intersection theorem

2 different lines intersect in at most ONE POINT

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plane determination theorem

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

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midpoint theorem

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

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Angle Bisector theorem

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

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supplementary theorem

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

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verticle angle theorem

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

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2-4 theorem

perpendicular lines form congruent adjacent angles.

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2-5 theorem

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

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2-6

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

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supplements of congruent angles theorem

supplements of congruent angles are congruent

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compliments of congruent angles theorem

compliments of congruent angles are congruent

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