Term
PointLinePlane Postulate
a. Unique line Assumption 

Definition
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Through any two points, there is exactly one line. 


Term
PointLinePlane Postulate
b. Number line assumption 

Definition
Every line is a set of points that can be put into a 1 to 1 correspondence with the real numbers, with any point on it corresponding to 0 and any other point corresponding to 1. 


Term
PointLinePlane Postulate
c. Dimension Assumption 

Definition
1. Given a line in a plane, there is at least 1 point in the plane that is not on the line.
2. Given a plane in space, there is at least one point in space that is not in the plane 


Term
PointLinePlane Postulate
d. Flat Plane Assumption 

Definition
If two points lie in a plane, the line containing them lies in the plane 


Term
PointLinePlane Postulate
e. Unique Plane Assumption 

Definition
Through three noncollinear points, there is exactly 1 plane. 


Term
PointLinePlane Postulate
f. Intersecting Plane Assumption 

Definition
If two different planes have a point in common, then their intersection is a line. 


Term
Distance Postulate
a. Uniqueness Property 

Definition
On a line, there is a unique distance between two points 


Term
Distance Postulate
b. Distance Formula 

Definition
If the two points on a line have coordinates x and y, the distance between them is [x  y] 


Term
Distance Postulate
c. Additive Property 

Definition
If B is on segment AC, then AB + BC = AC. 


Term
Triangle Inequality Postulate


Definition
The sum of the lengths of any two sides of a triangle is greater than the length of the third side 


Term
Angle Measure Postulate
a. Unique Measure Assumption 

Definition
Every angle has a unique measure from 0 to 180 


Term
Angle Measure Postulate
b. Unique Angle Assumption 

Definition
Given any ray VA and any real number r between 0 and 180, there is a unique angle BVA in each halfplane of line VA such that the measure of angle BVA = r. 


Term
Angle Measure Postulate
c. Zero Angle Assumption 

Definition
If ray VA and ray VB are the same ray, then the measure of angle AVB = 0. 


Term
Angle Measure Postulate
d. Straight Angle Assumption 

Definition
If VA and VB are opposite rays, then the measure of angle AVB = 180 


Term
Angle Measure Postulate
e. Angle Addition Property 

Definition
If ray VC (except for point V) is in the interior of angle AVB, then the measure of angle AVC + measure of angle CVB = the measure of angle AVB 


Term
Postulates of Equality
a. Reflexive Property of Equality
b. Symmetric Property of Equality
d. Transitive Property of Equality 

Definition
a. a = a (dumb property)
b. If a = b then b = a
c. If a = b and b = c then a = c 


Term
PointLinePlane Postulate
a. Unique line Assumption 

Definition
Through any two points, there is exactly one line. 


Term
Addition Property of Equality 

Definition
If a = b, then a + c = b + c 


Term
Multiplication Property of Equality 

Definition


Term
Postulate of Inequality
Transitive Property of Inequality 

Definition
If a is less than b and b is less than c, then a is less than c. 


Term
Addition Property of Inequality 

Definition
If a is less than b, then a + c is less than b + c. 


Term
Multiplication Properties of Inequality 

Definition
If a is less than b and c is greater than 0, then ac is less than ab
If a is less than b and c is less than 0, then ac is greater than ab 


Term
Postulate of Inequality Property 

Definition
If a and b are postive numbers and a + b = c, then c is greater than a and c is greater than b. 


Term

Definition
If a = b, then a may be substituted for b in any expression. 


Term
Corresponding Angles Postulate
Suppose two coplanar lines are cut by a transversal 

Definition
a. If two corresponding angles have the same measure, then the lines are parallel.
b. If the lines are parallel, then corresponding angles have the same measure. 


Term
Reflection Postulate
ABCD postulate 

Definition
a. Angle measure is preserved. b. Betweenness is preserved
c. Collinearity is preserved.
d. Distance is preserved.
e. 1 to 1 correspondence
f. Orientation is reversed 

