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5.1 Indirect Proof. Objective: After studying this section, you will be able to write indirect proofs. An indirect proof is useful when a direct proof is difficult to apply. Let’s take a look. A. D. B. E. C. F. Given:. Prove:. Proof: Either or. Let’s assume.
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5.1 Indirect Proof Objective: After studying this section, you will be able to write indirect proofs.
An indirect proof is useful when a direct proof is difficult to apply. Let’s take a look. A D B E C F Given: Prove: Proof: Either or Let’s assume
From the given information we can prove the triangles congruent by ASA, which makes But this is not possible, since the given information states that Therefore, our assumption was false and , because this is the only other possibility.
Indirect Proof Procedures 1. List the possibilities for the conclusion. 2. Assume that the negation of the desired conclusion is correct. 3. Write a chain of reasons until you reach an impossibility. This will be a contradiction of either: a. Given information or b. a theorem, definition, or other known fact. 4. State the remaining possibility as the desired conclusion.
Remember to start by looking at the conclusion! P Given: S R Q Prove:
C B A Given: O O Prove:
Summary In your own words describe how to write an indirect proof. Homework: worksheet
