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Axioms cannot be proved.
No. A corollary is a statement that can be easily proved using a theorem.
Neither. It is a hypothesis which may be true until proved or proved to be false.
Euclid was the one who proved that there are only five platonic solids.
If the number can be expressed in the form a/b where a and b are both integers and b ≠ 0, then it is proved rational. If you want to prove that it is irrational, then there are many complicated and different steps depending on the type of irrational number. (Yes there are different types)