No. Postulates are the foundations of geometry. If you said they were wrong then it would be saying that Euclidean geometry is wrong. It is like if you asked how do we know that English is right. It is how the English language works. So no postulates do not need to be proven.
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Every statement apart from the axioms or postulates.
Postulates are statements that prove a fact. An example would be that 2 points create a line segment. You usually use postulates in proofs.
Yes, postulates are "given", as the bases for the construction of the system.
Axioms, or postulates, are accepted as true or given, and need not be proved.
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