1. 5.1 Indirect Proof Objective: After studying this section, you will be able to write indirect proofs.

2. An indirect proof is useful when a direct proof is difficult to apply. Let’s take a Given: Prove: A B C D E F Proof: Either or Let’s assume

3. But wait! This is not possible, since the given information states that Therefore, our assumption was false and we can now say, because this is the only other possibility. From the given information we can prove the triangles congruent by ASA, which makes

4. a. Given information or b. A theorem, definition, or other known fact. 4. State the remaining possibility as the desired conclusion. Indirect Proof Procedure… 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:

5. Remember to start by looking at the conclusion! Given: Prove: P S Q R

6. Proof: Either or Assume. Then we can say. Since, we know that, thus, triangle PSR is congruent to triangle QSR by ASA (Since ). This means by CPCTC, but this contradicts the given information that therefore the assumption must be false, leaving the only other possibility: P S Q R

7. Given: Prove: B A O C O Hang in there, one last example…

8. Summary In your own words describe how to write an indirect proof.

9. Homework Worksheet 5.1