Axiomatic Structure of Mathematical System (Postulates and Theorems) Flashcards
A quantity is equal to itself.
Reflexive Property
If A = B, then B = A.
Symmetric Property
If A = B and B = C, then A = C.
Transitive Property
If A = B, then A + C = B + C.
Addition Property of Equality
These are terms that we cannot precisely define but are accepted by definition.
Undefined Terms
These terms have formal definitions and are used to define mathematical concepts.
Defined Terms
A statement that is accepted as true without proof.
Axioms/Postulates
A statement that can be proven and used to prove other statements.
Theorem
A line contains at least two points.
Postulate #1
A plane contains at least three non-collinear points.
Postulate #2
Postulate #3
Through any two points, there is exactly one line.
Through any three non-collinear points, there is exactly one plane.
Postulate #4
If two points lie on the same plane, then the line joining them lies in that plane.
Postulate #5
Postulate #6
If two planes intersect, then their intersection is a line.
Theorem #1
If two lines intersect, then they intersect at exactly one point.
If a point lies outside a line, then exactly one plane contains both the line and the point.
Theorem #2
If two lines intersect, then exactly one plane contains both lines.
Theorem #3
The figure formed by two rays sharing a common endpoint.
Angle
The Latin word “Angulus” means ___.
Corners
What symbol is used to represent an angle?
📐
Angles are measured in ___.
Degrees or Radians
What are angles composed of?
Two arms (sides) and a vertex (common endpoint)
These are the two rays that extend from a common point and form the angle.
Arms
This is the specific point at which the two arms meet.
Vertex
