indirect proofs

Front

What is an indirect proof?

Back

An indirect proof is a method of proving a statement by assuming the opposite of what you want to prove and showing that this assumption leads to a contradiction.

Front

What is the first step in an indirect proof?

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The first step is to assume the negation of what you are trying to prove.

Front

What assumption is made to start the indirect proof of AB≅BC?

Back

Assume that AB≠BC.

Tags

CCSS.HSG.CO.C.9

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What is the second step in an indirect proof?

Back

The second step is to contradict the given using logical statements based on the initial assumption.

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What type of proof is used when there are only two possibilities?

Back

An indirect proof is used when there are only two possibilities; if one is false, the other must be true.

Front

How do you conclude an indirect proof?

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You conclude an indirect proof by showing that the assumption leads to a contradiction, thus proving the original statement true.

Front

What is a contradiction in the context of indirect proofs?

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A contradiction occurs when the assumption made leads to a situation that cannot be true, thereby proving the original statement.

Front

Why is assuming the negation important in indirect proofs?

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Assuming the negation is important because it allows you to explore the consequences of that assumption and find contradictions.

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Can indirect proofs be used in geometry?

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Yes, indirect proofs are commonly used in geometry to prove theorems and properties.

Front

What is the relationship between direct proofs and indirect proofs?

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Direct proofs establish the truth of a statement directly, while indirect proofs establish truth by showing that the opposite leads to a contradiction.