Proof
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
A proof is a logical argument that shows a mathematical statement is always true using definitions, postulates (axioms), previously proven theorems, and rules of logical reasoning.
Formal Definition:
A proof is a step-by-step explanation that demonstrates the truth of a geometric statement by using logical reasoning and accepted mathematical principles.
Key Characteristics:
Built on known facts: definitions, postulates, and theorems.
Uses deductive reasoning to connect statements logically.
Often presented in formats such as:
Two-column proofs
Paragraph proofs
Flowchart proofs
Example (Outline):
To prove that the base angles of an isosceles triangle are congruent, a proof would:
Start with the given triangle and known properties (e.g., two sides are equal).
Apply definitions and theorems (like the congruence of triangles).
Conclude that the base angles must be equal.
A proof ensures that a statement is not just believed to be true, but guaranteed to be true in every case under the given conditions.