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Questions and Answers
What is the use of an indirect proof?
What is the use of an indirect proof?
An indirect proof is often used to prove theorems.
Which of the following statements are true? (Select all that apply)
Which of the following statements are true? (Select all that apply)
- Seven is a prime number. (correct)
- A right angle measures < 90° (correct)
- Apples make good pies (correct)
- A line contains at least two points. (correct)
- The sun is hot today. (correct)
- 3 + 2 = 7
What can be proven indirectly regarding triangles?
What can be proven indirectly regarding triangles?
A triangle cannot have two right angles.
What does an indirect proof assume?
What does an indirect proof assume?
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In an indirect proof, it is essential to reach a _____________ of a known fact.
In an indirect proof, it is essential to reach a _____________ of a known fact.
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What does the expression 'an established fact' refer to?
What does the expression 'an established fact' refer to?
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Study Notes
Indirect Proof Overview
- Indirect proofs are often employed to demonstrate the validity of theorems.
Key Characteristics of Indirect Proofs
- Indirect proof assumes the negation of the conclusion is accurate.
- The purpose is to deduce a contradiction from this assumption, highlighting the fallacy of the initial premise.
Example Application
- To prove that a triangle cannot have two right angles:
- Begin with the assumption that a triangle has two right angles.
- Recognize that the sum of angles in any triangle is 180°.
- Conclude that having two right angles exceeds 180°, proving that a triangle cannot have two right angles.
Key Terminology
- Contradiction is a critical element in indirect proofs, confirming the initial assumption's falsehood.
- "An established fact" encompasses universally accepted propositions relevant to the proof process.
Additional Facts
- Basic geometrical truths serve as foundational stepping stones in indirect proofs; e.g., a right angle measures less than 90°, and a line must consist of at least two points.
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