Indirect proofs

Front

What is indirect reasoning?

Back

Indirect reasoning is a type of reasoning where one possibility is proven false, leading to the conclusion that the other possibility must be true.

Front

What is the first step to prove that an equilateral triangle does not have a right angle?

Back

The first step is to assume that the triangle has a right angle.

Front

What is an assumption in the context of indirect proofs?

Back

An assumption is to assume the opposite of what you want to prove.

Front

Define a rhombus.

Back

A rhombus is a quadrilateral with parallel, congruent sides.

Front

What is the first step to prove that we don't have homework tonight?

Back

The first step is to assume that we have homework tonight.

Front

What is the purpose of an indirect proof?

Back

The purpose of an indirect proof is to demonstrate that a statement is true by showing that assuming the opposite leads to a contradiction.

Front

How do you start an indirect proof?

Back

You start an indirect proof by assuming the opposite of what you want to prove.

Front

What is a contradiction in the context of indirect proofs?

Back

A contradiction is a situation where two or more statements or conclusions cannot all be true at the same time, often used to disprove an assumption.

Front

What is the relationship between assumptions and conclusions in indirect proofs?

Back

In indirect proofs, the assumption is the opposite of the conclusion you want to prove; if the assumption leads to a contradiction, the conclusion is validated.

Front

What is the significance of proving a statement indirectly?

Back

Proving a statement indirectly can provide a more robust understanding of the statement's validity by exploring its negation.