Like what you saw?
Create FREE Account and:
- Watch all FREE content in 21 subjects(388 videos for 23 hours)
- FREE advice on how to get better grades at school from an expert
- Attend and watch FREE live webinar on useful topics
Postulate, Axiom, Conjecture - ConceptFREE
Univ. of Wisconsin
J.D. Univ. of Wisconsin Law school
Brian was a geometry teacher through the Teach for America program and started the geometry program at his school
Three words that are used seemingly interchangeably in Geometry are postulate, axiom, and conjecture. It is important, however, to know how each word is different and to know the subtle implications of using each word. These terms are especially important when working with Geometry proofs.
Now that you're in geometry we are going to use three words that you probably didn't use in Algebra. They are postulate, axiom, and conjecture. And they get confusing when to use one and not the other. While, postulate or an axiom is an accepted statement of fact, there is nothing that you can prove wrong about it, a conjecture is a conclusion derived from inductive reasoning. Well inductive reasoning, if I draw a line under that, is the process of observing patterns and making generalizations so not everyone is going to be true.
Well, what is an example of a postulate or an axiom? If you look over here, a postulate of an axiom could say through any two points there exists only one line. Well, if I think about two points somewhere there is only one possible line that will go through both of those points. So there's an accepted statement of fact here that I cannot prove incorrect.
What about a conjecture? Remember; conjecture we said was a conclusion derived from inductive reasoning.
LetÂ’s say one day you're bored during class and you realized that one squared was equal to one so the original number is equal to two the square number. Two squared is equal to four, three squared is equal to nine, so you make the conjecture that the square of any number is larger or equal to the original number. Well that would be a conjecture because you're noticing this pattern and you're making a statement based on that.
Well I am going to say, what about one half? If you square one half you're going to get one fourth and one fourth is not larger than one half.
So a conjecture is not always true and it's based on inductive reasoning. A postulate or an axiom is an accepted statement of fact where you'll not be able to find any counter example.
Stuck on a Math Problem?
Ask Genie for a step-by-step solution
Please enter your name.
Are you sure you want to delete this comment?
- Using a Protractor 21,162 views
- Angle Bisectors 17,686 views
- Supplementary and Complementary Angles 25,867 views
- Polygons 17,277 views
- Types of Triangles 20,806 views
- Perimeter 11,576 views
- Parts of a Circle 14,598 views
- Three Undefined Terms: Point, Line, and Plane 66,255 views
- Counterexample 27,641 views
- Writing a Good Definition 17,813 views
- Converse 15,199 views
- Line Segments 34,462 views
- Rays 25,007 views
- Parallel and Skew Lines 31,873 views
- Midpoints and Congruent Segments 25,726 views
- Parallel Planes and Lines 23,518 views
- Vertex and Diagonals 16,248 views
- Calculating the Midpoint 20,999 views
- Angles: Types and Labeling 24,739 views