What term describes a statement that follows from a previous result?

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

Answer: (C)

A corollary is a statement that follows directly from a previously proven result. Once you’ve established a theorem, you can often derive related facts with little or no extra work because the new statement flows naturally from what you’ve already proved.

Think of it this way: the theorem is the main result you’ve proven, and a corollary is a natural consequence that you can deduce from that theorem. For example, if you prove that the sum of the interior angles in a triangle is 180 degrees, a corollary is that an exterior angle equals the sum of the two opposite interior angles—the result follows directly from the angle-sum theorem.

Axioms are the starting assumptions you take as given, not proven; a theorem is a statement you prove from those axioms; and a proof is the justification you provide to establish a theorem. The corollary sits beside the theorem as a related, easily derived consequence.