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?

Back

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.

Front

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.

Front

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?

Back

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?

Back

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?

Back

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

Front

Can indirect proofs be used in geometry?

Back

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

Front

What is the relationship between direct proofs and indirect proofs?

Back

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