No axiom, postulate, definition, or theorem of geometry may contradict another, nor may it ever contradict any conclusion reached with the help of other axiom, postulate, definition, etc. In contrast, a paradox is a statement that leads to self-contradictory conclusions. For instance, Russell’s paradox is the most famous of the logical or set-theoretical paradoxes: Consider the set of all sets that are not members of themselves. Such a set appears to be a member of itself
if and only if it is not a member of itself. Hence the paradox.

Research more about paradoxes and discuss one real-life example and one geometric example (excluding Russell’s Paradox).