Definitions, Theorems, Properties, & Postulates
Correct Segment Notation
We can say segments are congruent.
Correct Angle Notation
We can say angles are congruent.
We say lengths of segments are equal.
We say measures of angles are equal.
*Remember Definitions work both ways. They are biconditional statements!
Name of Definition
What it tells you…
Definition of Congruence
If two things are equal then they are congruent.
Definition of a Midpoint
The point that divides a segment into two congruent segments.
Definition of a
Segment Bisector
A point, ray, line, line segment, or plane that intersects the
segment at its midpoint.
Definition of an Angle
Bisector
A ray that divides an angle into two congruent angles.
Definition of
Complementary Angles
Two angles whose sum is 90°.
Definition of
Supplementary Angles
Two angles whose sum is 180°.
Definition of Vertical Angles
Two angles that are opposite each other when two lines
intersect.
Definition of a Linear Pair
Two adjacent angles whose non-common sides are opposite rays.
Definition of
Perpendicular Lines
Two lines that intersect to form a right angle.
Definition of Right Angles
All right angles are 90°.
Name of Theorem
What it tells you…
Right Angle Theorem
All right angles are congruent.
Vertical Angles Theorem
Vertical angles are congruent.
Let a, b, and c be real numbers
Name of Property
What it tells you…
Addition Property
If 𝑎 = 𝑏, then
Subtraction Property
If 𝑎 = 𝑏, then
Multiplication Property
If 𝑎 = 𝑏, then
Division Property
If 𝑎 = 𝑏, then
Distributive Property
If 𝑎 = 𝑏, then
Substitution Property
𝑎(𝑏 + 𝑐) =
Reflexive Property
Segments: AB = AB
Angles: m∠1 = m∠1
Symmetric Property
Segments:
If AB = CD, then CD = AB.
Angles:
If m∠1 = m∠2, then m∠2 = m∠1.
Transitive Property
Segments:
If AB = CD and CD = EF,
then AB = EF.
Angles:
If m∠1 = m∠2 and m∠2 = m∠3,
then m∠1 = m∠3.
Name of Postulate
What it tells you…
Segment Addition Postulate
If point B is between A and C, then AB + BC = AC.
Angle Addition Postulate
The sum of two adjacent angle measures is equal to the
measure of the larger angle.
Linear Pair Postulate
Linear pairs are supplementary.