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A corollary is a theorem whose proof is a direct consequence of another theorem, axiom, or definition. For example, the corollary below follows from the Triangle Angle Sum Theorem.
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Triangle Angle Sum Corollary |
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There can be at most one right or obtuse angle in a triangle. |
Proofs of corollaries are often short or even not required. Similar to theorems, corollaries can be reasons in a deductive reasoning. Therefore, a corollary can be used in proofs of other corollaries or theorems.