Download List of Theorems, Postulates and Definitons 1

Section 1.2-1.3
Definition
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.
Definition
Betweenness-The number between two other numbers if it is
greater than one of them and less than the other
Section 2.1
Definitions
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-The values that are common between two
numbers
Section 3.1-3.3
Definitions
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 equal two lines.
Theorems
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
Postulate
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
Theorem
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
Section 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
Theorems
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.
Section 4.1
Definition
Transformation- Two sets of points that each point in preimage set
Section 4.2
Postulate
Reflection Postulate- Reflection preserve: Angle measure,
betweenness co-linearity, distance
Section 4.4
Definition
Composite- The first transformations of a figure, then an
additional transformation
Magnitude- The distance between two points
Section 4.6
Definition
Vector – Magnitude and direction of a translation
Section 4.7
Definition
Isometric- Reflection or composite of a reflection
Section 5.5
Theorem
Figure reflection theorem- The reflection image is
corresponding if the angle has reflected points
Section 5.6
Definitions
Auxiliary Figures- Objects we add to a diagram to prove a
statement
Uniqueness- One and exactly one point or definition
Section 5.7
Theorem
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