5-4 Indirect Proof

Front

What is the first step of an indirect proof?

Back

Assume the negation of what you are trying to prove.

Front

What is another name for proof involving indirect reasoning?

Back

Indirect Proof or Proof by Contradiction.

Front

What is a counterexample?

Back

An example that shows a statement is false.

Front

What assumption would you make to start the indirect proof of: there can be only one 90 angle in a triangle?

Back

Assume there can be more than one 90 angle in a triangle.

Front

What assumption would you make to start the indirect proof of AB≅BC?

Back

Assume AB≠BC.

Front

What is the purpose of an indirect proof?

Back

To show that assuming the opposite of what you want to prove leads to a contradiction.

Front

In an indirect proof, what does it mean to assume the negation?

Back

It means to take the opposite of the statement you are trying to prove.

Front

What is a contradiction in the context of an indirect proof?

Back

A statement that is logically inconsistent with the assumptions made.

Front

How does an indirect proof differ from a direct proof?

Back

An indirect proof assumes the opposite of the conclusion and shows that this leads to a contradiction, while a direct proof shows the conclusion is true through logical steps.

Front

What is the significance of a counterexample in proofs?

Back

It demonstrates that a general statement is false by providing a specific case where it does not hold.