Geometry [Lesson 5-4 : Indirect Truth] and [Lesson 5-5 : The Triangle Inequality]

5.11 Triangle Inequality Theorem

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

FALSE. A counterexample helps you disprove a conjecture. It cannot be used to prove a conjecture.

True or False : Proof by contradiction and using a counterexample are the same. Why?

DIRECT PROOF

assume that p is true by using the rules of inference, axioms, and logical equivalences to show that q must also be true

PROOF BY CONTRADICTION

indirect proof, in which one assumes that the statement to be proved is false

INDIRECT PROOF

proof in which a statement to be proved is assumed false and if the assumption leads to an impossibility, then the statement assumed false has been proved to be true

INDIRECT REASONING

reasoning that assumes the conclusion is false and then shows that this assumption leads to a contradiction of the hypothesis, like a postulate, theorem, or corollary; since the assumption has been proved false, the conclusion must be true