## Two Column Proof Definition:

`This consists of a list of statements, and the reasons that we know those statements are true. The two column proof has five parts:`

1) Given

2) Proposition

3) Statement Column

4) Reason Column

5) Diagram

## Two Column Proof Example 1:

Given: ∠A and ∠B are complementary and ∠A ≅ ∠C

Prove: ∠A and ∠C are supplementary

Statement | Reason |
---|

∠A and ∠B are complementary | Given |

m∠A + m∠B = 90° | Definition of Complementary Angles |

∠A ≅ ∠C | Given |

m∠A ≅ m∠C | Definition of Congruent Angles |

m∠C + m∠B = 90° | Substitution Property of Equality |

∠C and ∠B are complementary | Definition of Complementary Angles |

## Two Column Proof Example 2:

Given: ∠1 and ∠2 are right angles

Prove: ∠1 ≅ ∠2

Statement | Reason |
---|

∠1 and ∠2 are right angles | Given |

m∠1 = 90° and m∠2 = 90° | Definition of Right Angle |

m∠1 = m∠2 | Transitive Property of Equality |

∠1 ≅ ∠2 | Definition of Congruent Angles |

## Two Column Proof Example 3:

Given: ABCD is a square

Prove:

DB ≅

CAStatement | Reason |
---|

ABCD is a square | Given |

DA ≅ BC | Definition of Square |

DC ≅ BA | Definition of Square |

∠D ≅ ∠B | Definition of Parallelogram |

∠ADC ≅ ∠CBA | SAS Congruence |

DB ≅ CA | CPCTC |

### How does the Two Column Proof Calculator work?

Shows you the details behind a two column proof including the five parts and examples

### What 4 concepts are covered in the Two Column Proof Calculator?

- given
- A thing or set of things helpful in forming a conclusion or judgment
- proof
- an inferential argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion
- proposition
- a declarative sentence that is either true or false (but not both)
- two column proof
- This consists of a list of statements, and the reasons that we know those statements are true. The two column proof has five parts:

1) Given

2) Proposition

3) Statement Column

4) Reason Column

5) Diagram

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