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# 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.

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