GeoGebra Classroom

# Indirect Proof Introduction

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

1. What is the capital of Mali?

Select all that apply
• A
• B
• C
• D

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

Select all that apply
• A
• B
• C
• D

3. Which person won a Nobel Prize twice?

Select all that apply
• A
• B
• C
• D

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?

Select all that apply
• A
• B
• C
• D

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

Select all that apply
• A
• B
• C
• D

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

Select all that apply
• A
• B
• C
• D

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?

Select all that apply
• A
• B
• C
• D

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?

Select all that apply
• A
• B
• C
• D

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?

Select all that apply
• A
• B
• C
• D