Indirect Proof Introduction

Author:
powere

Determine the correct answer to the questions below by indirect reasoning.

1. What is the capital of Mali?

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2. Which Italian scientist used a new invention called the telescope to discover the moons of Jupiter?

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3. Which person won a Nobel Prize twice?

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Take a few minutes to explore Indirect Proofs in Geometry on the internet to get an idea of what an indirect proof is. Please type your initial thoughts below along with an example. You do not need to explain the entire proof you may write "An example of an indirect proof would be proving that......" and provide an example.

4a. If your friend Sally enters your house carrying a dry umbrella, what can you conclude?

4b. Assume for a moment that your friend Sally walked to your house in a rain storm. What can you conclude about Sally's umbrella?

4c. Does your answer to question 4b contract the given information in question 4a about Sally's dry umbrella?

Question 4 above is an example of an indirect proof. We reached a contradiction because if it was raining outside then Sally's umbrella would have been wet, but it was dry.

Steps for Writing an Indirect Proof: (Fill in the blanks)

1. Assume temporarily that ____________________. 2. Proceed with definitions and given information. 3. Reach a __________________. 4. Since we reached a contradiction, the assumption is ________. 5. Since our assumption is false, our original statement must be ______.

5. If you are trying to prove that triangle ABC is equilateral using an indirect proof, what would be the first sentence in your proof?

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6. If you are trying to prove that Doug is Canadian using an indirect proof, what would be the first sentence in your proof?

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7. If you are trying to prove that using an indirect proof, what would be the first sentence in your proof?

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8. If you are trying to prove that Kim isn't a violinist using an indirect proof, what would be the first sentence in your proof?

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9. If you are trying to prove that (m<A) > (m<Y) using an indirect proof, what would be the first sentence in your proof?

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10. If you are trying to prove that segment CX isn't a median of triangle ABC using an indirect proof, what would be the first sentence in your proof?

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11. Planning to write an indirect proof that <A is an obtuse angle, Becky began by saying "Assume temporarily that angle A is an acute angle". What has she overlooked?

12. Planning to write an indirect proof to prove that m and n are skew lines, John began by assuming that m and n are intersecting lines. What has he overlooked?

Fill in the blanks for the following proof.

13. Given: n is an integer is even Prove: n is even Proof: a. Assume temporarily that n is ________. b. Since n is not even, then n must be _______. c. = n*n = odd*odd = ______. d. Therefore, is ______. e. However, this contradicts part of our given information that is _______. f. Therefore, the temporary assumption that n is not even must be ________. g. Thus we have proven that n is _______.