# Definitions, Postulates, and Theorems

## Terms

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- Postulate 1- (Ruler Postulate)
- 1. Points on a line can be assigned numbers like 0 and 1... 2. The distance between points is (absolute value of) x-y.
- Postulate 2- (Segment Addition Postulate)
- If B is between A and C, then AB+BC=AC.
- Postulate 3- (Protractor Postulate)
- If ray OB and ray OA are opposite rays and we make ray OA=0 degrees and ray OB=180 degrees, then we create a protractor.
- Postulate 4- (Angle Addition Postulate)
- 1. If B is on the interior of angle COA, then the measure of angle COB plus the measure of angle BOA= angle COA. 2. If angle COA=180 degrees, then the measure of angle COB+ the measure of angle BOA=180 degrees.
- Postulate 5
- A line contains at least 2 points, a plane contains at least 3 points, space has at least 4 points, not all in the same plane.
- Postulate 6
- Thru any 2 points there is exactly 1 line.
- Postulate 7
- Thru any 3 points there is at least 1 plane, if they are non-collinear, there is only 1 plane that runs thru them.
- Postulate 8
- If 2 points are in a plane, then the line containing them is also in the plane.
- Postulate 9
- If 2 planes intersect, the intersection is always a line.
- Theorem 1-1
- If 2 lines intersect, their intersection is a point.
- Theorem 1-2
- Thru a line, and a point not on the line, there is exactly one plane.
- Theorem 1-3
- If 2 lines intersect, then exactly 1 plane contains the 2 lines.
- Theorem 2-1 (Midpoint Theorem)
- If M is the midpoint of segment AB, then AM=1/2AB and MB=1/2AB.
- Theorem 2-2 (Angle Bisector Theorem)
- If ray BX is the bisector of angle ABC, then the conclusion can be made that the measure of angle ABX=1/2 the measure of angle ABC and the measure of angle XBC=1/2 the measure of angle ABC.
- space plane collinear noncollinear
- all points together flat surface 3 or more points that make up a line 3 or more points that don't make a line
- opposite rays congruent bisector congruent angles adjacent angles
- 2 rays that form a straight line same shape, same size split into 2 equal parts same degrees common side, 2 common vertex
- conditionals converse biconditional
- general form: if p, then q the reversal of a conditional conditional and its converse are both true
- Addition Property of Equality
- If 2 #'s are equal (a=b) and 2 other #'s are equal (c=d), then a+c=b+d
- Subtraction Property of Equality
- If a=b and c=d, then a-c=b-d.
- Multiplication Property of Equality
- A=B, therefore A times C= B times C.
- Division Property of Equality
- A=B, therefore A/C=B/C.
- Substitution Property of Equality
- It a=b, they are interchangeable.
- Distributive Property of Equality
- 3(a+b)=3a+3b.
- Reflexive Property of Equality
- a=a
- Summetric Property of Equality
- If a=b, then b=a.
- Transitive Property of Equality
- If a=b and b=c, then a=c
- Reflexive (congruency)
- Angle x is congruent to angle x.
- Symmetric (congruency)
- If segment XY is congruent to segment RT, then segment RT is congruent to segment XY.
- Transitive (congruency)
- If angle A is congruent to angle N, and angle N is congruent to angle Z, then angle A is congruent to angle Z.