Introduction to Deductive Proof
Deductive proof uses logical reasoning from known facts (axioms and theorems) to prove that a new statement must be true. It is the foundation of rigorous mathematics.
What You Need to Know
Key Concept Diagram
A deductive proof starts from accepted facts and uses logical steps to reach a conclusion
Every step must be justified with a reason (theorem, definition, or given information)
Proof by counterexample disproves a statement by finding one case where it fails
Geometry proofs often use angle theorems and congruence conditions as reasons
Key Vocabulary
Deductive reasoning
Drawing conclusions by applying general rules to specific cases
Axiom
A statement accepted as true without proof; a starting assumption
Theorem
A statement that has been proven to be true using logical argument
Counterexample
A single example that disproves a general statement
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
In a proof, you write: "Angle ABC = Angle DEF (corresponding angles, parallel lines)". What does the part in brackets represent?
Question 2
A student claims all prime numbers are odd. Which counterexample disproves this?
Question 3
What is the first step in a geometric proof?
Key Concepts Summary
- ●A deductive proof starts from accepted facts and uses logical steps to reach a conclusion
- ●Every step must be justified with a reason (theorem, definition, or given information)
- ●Proof by counterexample disproves a statement by finding one case where it fails
- ●Geometry proofs often use angle theorems and congruence conditions as reasons