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.
Lets 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.