Download List of Theorems, Postulates and Definitions 3

Section 1.2 and 1.3
Definitions
Dense- Numbers go on forever and there are an infinite number of numbers between two numbers.
Section 1.8
Postulates
Uniqueness property- There is an exact distance between two points.
Additive property- If B is between line AC then AB+BC=AC.
Definitions
Betweeness- The number between two other numbers if it is greater than one of them and less than
the other
Section 2.1
Definition
Convex figure- A figure with no holes or dents in the side of the figure
IFF- If and only if
Conditionals => Flip the hypothesis and conclusion example: p=>q
Bi-conditionals  If and only if the conditional and converse are true
Union- The values between two numbers
Intersections- What values are common between two numbers
Section 3.1 and 3.3
Definition
Angle Bisector- A ray that goes between angles
Complementary angles- Two angles that equal 180 degrees
Supplementary angles- Two angles that equal 90 degrees
Adjacent angles- Two rays that end with a common end point.
Linear pair- Two adjacent angles that are on non-common sides and opposite rays
Vertical angles- Non-straight angles when the union of their sides are two lines.
Theorem
Linear pair theorem- Two angles that form a linear pair, they are supplementary
Vertical angles theorem- Two angles that are vertical, then they are equal
Postulates
Angle addition postulate- <ABD+<DBC=<ABC
Section 3.4
Postulates
Reflexive property- a=a
Symmetric property- If a=b, then b=a
Transitive property- If a=b and b=c then a=c
Substitution property- If a=b and b=c then a can equal c
Multiplication property- Multiply or divide both sides an equation by the same number
Section 3.5
Definitions
Justifications- 3 types, Postulates, property and definition
Section 3.6
Theorems
C.A.P- Two lines are parallel if corresponding angles created by a transversal are equal.
Definition
Transversal- A line that intersects two other lines
3.7
Theorems
Parallel and slope theorem- Slopes of parallel lines are equal
Perpendicular and slope theorem- Slopes of perpendicular lines are opposite reciprocals
Section 3.8
Theorem
Two perpendicular theorem- Two coplanar lines are each perpendicular to the same line, they are
parallel.
Perpendicular to parallel theorem- If a line is perpendicular to one of two parallel lines, then it is also
perpendicular to the other.
4.1
Definition
Transformation- Two sets of points that each point in pre-image set
4.2
Postulate
Reflection Postulate- Reflection preserve: Angle measure, betweeness co-linearity, distance
4.4
Definition
Composite- The first transformations of a figure, then an additional transformation
Magnitude- The distance between two points
4.6
Definition
Vector – Magnitude and direction of a translation
4.7
Definition
Isometric- Reflection or compostite of a reflection
5.5
Figure reflection theorem- The reflection image is corresponding if the angle has reflected points
5.6
Auxiliary Figures- Objects we add to a diagram to prove a statement
Uniqueness- One and exactly one point or definition
5.7
Triangle Sum Theorem- The sum of the angles measure of three angles is 180 degrees.
Any other polygon- 180(n-2)
N=number of sides