Indirect Proof (Section 5-4)

Front

What is an indirect proof?

Back

A proof that assumes the negation of the statement to be proven is true, leading to a contradiction.

Front

What is the first step in an indirect proof?

Back

Assume the negation of the statement to be proven is true.

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 is the relationship between an exterior angle of a triangle and its remote interior angles?

Back

The exterior angle is greater than either of its remote interior angles.

Front

What is the conclusion of an indirect proof?

Back

To show that the assumption made leads to a contradiction, thus proving the original statement true.

Front

What is the difference between direct proof and indirect proof?

Back

Direct proof establishes the truth of a statement directly, while indirect proof shows that assuming the opposite leads to a contradiction.

Front

In an indirect proof, what does it mean to contradict a known fact?

Back

It means to show that the assumption made in the proof leads to a situation that is impossible or false.

Front

If 3x + 7 > 13, what assumption would you make to start the indirect proof?

Back

Assume x ≤ 2.

Front

What is a contradiction in the context of indirect proof?

Back

A statement that is logically inconsistent with the assumptions made in the proof.

Front

How can indirect proof be used in geometry?

Back

It can be used to prove properties of shapes, such as the uniqueness of angles in triangles.