A contradiction is a statement that is necessarily false. For example, if a proof starts with the assumption that line segment AB is less than line segment CD, and later concludes that AB = CD, both statements can not be true at the same time. One statement contradicts the other.
A proof by contradiction starts with a statement that is to be disproved. It then proceeds to show the statement false by arriving at a contradiction. An example of a proof by contradiction is Euclid's proof that if two angles are equal, then the sides opposite the equal angles are also equal. A proof by contradiction can also be called an indirect proof, or reductio ad absurdum (Latin for "reduction to the absurd").
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