Corollary to a Theorem
See It in Action
Two examples of the idea done right—and one common look-alike that is not right.
EXAMPLE
EXAMPLE
NON-EXAMPLE
Definition
Corollary to a Theorem: A corollary is a statement that follows directly from a previously proven theorem and can be proved with little or no additional work.
Key points:
A corollary is usually a “bonus” result that comes from a theorem.
It is considered true because the theorem it follows has already been proven.
Often, corollaries simplify or extend the application of a theorem.
Example:
Theorem: The sum of the angles in a triangle is 180°.
Corollary: Each angle of an equilateral triangle measures 60°.
Why it’s a corollary:
Once the theorem about the sum of angles is proven, it immediately follows that if all three angles are equal (equilateral triangle), each must be 180° / 3 = 60°.
Very little additional proof is needed beyond the original theorem.