**Example** of an Indirect Proof

Prove that $$ \angle $$BDA is not a straight angle.

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

1) $$ \angle $$BDA is a straight angle |
1) (Assume opposite) |

2) m $$ \angle $$BDA = 180° | 2) Definition of a straight angle |

3) AD $$ \perp $$ BC | 3) Given |

4) $$ \angle $$BDA is a right angle | 4) Definition of perpendicular lines |

5) m $$ \angle $$BDA = 90° | 5) Definition of a right angle |

6) m $$ \angle $$BDA is not a straight angle |
6) Contradiction of steps 2 and 5 |

7) $$ \angle $$BDA is not a straight angle | 7) Due to the contradiction between 2 and 5, we know that the assumption that WE INTRODUCED in the first step ($$ \angle $$bda is a straight angle) is false. Therefore, the opposite must be true: $$ \angle $$ is not a straight angle. |