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Postulates and axioms are accepted without proof in a logical system. Theorems and corollaries require proof in a logical system.
Pythagorean's Theorem is one of the most famous ones. It says that the two squared sides of a right triangle equal the squared side of the hypotenuse. In other words, a2 + b2 = c2
If they are known not to be true then they are no longer postulates but discarded theories.
The size of the shape changes with a similarity transformation (enlargement), whereas it does not with a congruence transformation.
True. Axioms and postulates do not require proof to be used.