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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
In Geometry, a theorem is:
“A statement that can be proven true using logic, definitions, postulates, and previously proven theorems.”
Key characteristics:
A theorem is not just assumed to be true — it requires proof.
It is a logical conclusion based on accepted facts.
Theorems are often used to prove other, more complex theorems.
Example:
The Vertical Angles Theorem: Vertical angles are congruent.
This isn’t just assumed — it’s proven using geometric reasoning.
Compare to a postulate:
Postulate: Accepted without proof
Theorem: Must be proven to be accepted as true
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