# Indirect Proof

See how to prove a statement

by using indirect proof.

1 example and its solution.

## Indirect Proof

### Definition

Statement | Reason |
---|---|

~Prove | Assumption |

↓ | |

Prove | Contradiction |

is another way to prove a statement.

Instead of proving a statement directly,

you show a contradiction

to prove a statement indirectly.

How to:

Assume that ~prove is true.

Then show a contradiction.

This is made by the wrong assumption:

~Prove.

→ ~Prove: ( x )

→ Prove: ( o )

Logic (Geometry)

Two-Column Proof

### Example

Given: AM ≠ MB

Prove: M is not the midpoint of AB

Solution Prove: M is not the midpoint of AB

Given: AM ≠ MB

Prove: M is not the midpoint of AB

Prove: M is not the midpoint of AB

Statement | Reason |
---|---|

1. M is the midpoint of AB. | Assumption |

2. AM ≌ MB | The midpoint divided the segment into two congruent segments. |

3. AM = MB | Definition of congruent segments |

4. AM ≠ MB | Given |

5. M is not the midpoint of AB. | Contradiction: 3, 4 The assumption is false and its negation is true. |

5. The assumption,

M is the midpoint of AB,

is false.

And its negation (Prove),

M is not the midpoint of AB,

is true.

So Prove is true.

M is the midpoint of AB,

is false.

And its negation (Prove),

M is not the midpoint of AB,

is true.

So Prove is true.

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