A corollary is best described as which of the following?

• A. Theorem
• B. Proof
• C. Corollary
• D. Axiom

Answer: (C)

A corollary is a result that follows directly from a proven theorem, usually with little or no extra proof needed. It’s a neat, immediate consequence of what you’ve already shown, so once the main theorem is established, the corollary essentially falls out of it.

For example, from a theorem stating that the sum of the angles in any triangle is 180 degrees, a corollary is that the exterior angle equals the sum of the two opposite interior angles. This is a direct consequence that doesn’t require a substantial new argument.

This differs from a theorem, which is a major statement that requires its own proof; a proof is the logical justification of a statement; and an axiom is a basic assumption accepted without proof. So a corollary is best described as an immediate consequence of a proven result.