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What do you call a statement in geometry that requires proof?
Theorems are statements in geometry that require proof.
What is the difference between proof and postulate?
A proof uses postulates and theorems to prove some statement.
Can a theorem justify a statement in a geometric proof?
Yes. That is what theorems are for. Once proven, their results do not need to be justified again (except for exams).
Is every statement a theorem why?
There are many kinds of statement that are not theorems: A statement can be an axiom, that is, something that is assumed to be true without proof. It is usually self-evident, but like Euclid's parallel postulate, need not be. A statement need not be true in all circumstances - for example, A*B = B*A (commutativity) is not necessarily true for matrix multiplication. A statement can be false. A statement can be self-contradictory for example, "This statement is false".
What does theorem mean in geometry?
A theorem is a statement or proposition which is not self-evident but which can be proved starting from basic axioms using a chain of reasoned argument (and previously proved theorems).
