in geometry, why is the hinge theorem called that and what is the difference between theorems and postulate?

Answer 1

A postulate is something that is so obvious it is accepted as true without proof. For example, A straight line , and only one straight line can be drawn between two points is a postulate that is accepted as true without proof.

A Theorem is a hypothesis or statement that is to be proven or disproved. It is never accepted as true without rigorous proof.

The Hinge theorem is called that because one of the sides of a triangle can swing like a hinge into two different positions that could solve a triangle problem.

Answer 2

Hinge Theorem

Answer 3

You should be aware that theorems in elementary geometry textbooks often have names that are not standard. I am not familiar with the hinge theorem, at least by that name, and I have a degree in mathematics and have taught high school geometry for several years.

Answer 4

postulate is a proof that doesn't need to be proved. For example, midpoint postulate. As you know, any segment that has a midpoint then it has two small congruent segments. No body is gonna argue that.

Theorem is a proof that is proved. Just like, ASA is a postulate, they use that postulate to prove t tringles are congruent by AAS (AAS theorem)

Answer 5

every science is a philosophy that starts from basic axiomas that are said are self evident In traditional logic, an axiom or postulate is a proposition that is not proved or demonstrated but considered to be either self-evident, or subject to necessary decision. Therefore, its truth is taken for granted, and serves as a starting point for deducing and inferring other (theory dependent) truths Theoremas has to be demonstrated and once has been done are to help for further calculus to simpliy math work.... Converses are different point of view, that might help u to get a better ideea U can use any of them, as a well know reference point for others whichever one helps u solve the problem...

Answer 6

Postulates are statements that are assumed to be true without proof. Postulates serve two purposes - to explain undefined terms, and to serve as a starting point for proving other statements.

Theorums are statements that can be deduced and proved from definitions, postulates, and previously proved theorums.