Section 12.4 – Indirect Proof

Contradiction

p AND ~p

Proof by contradiction – to prove a statement is true, assume that the conclusion is false and show that this leads to a contradiction somewhere in the proof.

Examples]

Theorem

If two lines are cut by a transversal such that corresponding angles are congruent, then the two lines are parallel

Proof

Given: line is a transversal that intersects lines m and n, and.

Prove: m // n

Proof: Assume that m is not parallel to n. Therefore, m and n will intersect at a point, C. Because is an exterior angle of, . Since °, therefore . Therefore, . This is a contradiction to the given. So, our assumption that m is not parallel to n is false. Therefore, our conclusion is true. m // n

Contradiction: () AND ()