# Logic and Proof: Provin' and Groovin' Quiz

*? Put your knowledge to the test. Good luck — the Stickman is counting on you!*

**Logic and Proof**

*COD*and ∠

*COB*

*AOB*and ∠

*WOX*

*BOC*and ∠

*DOZ*

*WOX*and ∠

*DOC*

*BOA*and ∠

*XOY*

*XY*+

*YZ*=

*XZ*, what must we know about points

*X*,

*Y*, and

*Z*?

*X*is on segment

*YZ*

*Y*is on segment

*XZ*

*Z*is on segment

*XY*

*XYZ*and ∠

*YZX*are complementary

*Y*is the midpoint of

*XZ*

*X*and ∠

*Y*?

*X*≠ m∠

*Y*

*X*= 180 – m∠

*Y*

*X*≅ ∠

*Y*

*X*– m∠Y = 90

*Y*= 90

*CME*and ∠

*DMF*are congruent.

Statements | Reasons |

1. ∠CMD ≅ ∠AMB | Given |

2. ∠AMB and ∠FME are vertical angles | Given |

3. ∠AMB ≅ ∠FME | ? |

4. ∠CMD ≅ ∠FME | ? |

5. m∠CMD = m∠FME | ? |

6. m∠CMD + m∠DME = m∠FME + m∠DME | ? |

7. m∠CME = m∠DMF | ? |

8. ∠CME ≅ ∠DMF | ? |

Which of the following is the best reason for statement 3?

*CME*and ∠

*DMF*are congruent.

Statements | Reasons |

1. ∠CMD ≅ ∠AMB | Given |

2. ∠AMB and ∠FME are vertical angles | Given |

3. ∠AMB ≅ ∠FME | ? |

4. ∠CMD ≅ ∠FME | ? |

5. m∠CMD = m∠FME | ? |

6. m∠CMD + m∠DME = m∠FME + m∠DME | ? |

7. m∠CME = m∠DMF | ? |

8. ∠CME ≅ ∠DMF | ? |

Which of the following is the best reason for statement 4?

*CME*and ∠

*DMF*are congruent.

Statements | Reasons |

1. ∠CMD ≅ ∠AMB | Given |

2. ∠AMB and ∠FME are vertical angles | Given |

3. ∠AMB ≅ ∠FME | ? |

4. ∠CMD ≅ ∠FME | ? |

5. m∠CMD = m∠FME | ? |

6. m∠CMD + m∠DME = m∠FME + m∠DME | ? |

7. m∠CME = m∠DMF | ? |

8. ∠CME ≅ ∠DMF | ? |

Which of the following is the best reason for statement 5?

*CME*and ∠

*DMF*are congruent.

Statements | Reasons |

1. ∠CMD ≅ ∠AMB | Given |

2. ∠AMB and ∠FME are vertical angles | Given |

3. ∠AMB ≅ ∠FME | ? |

4. ∠CMD ≅ ∠FME | ? |

5. m∠CMD = m∠FME | ? |

6. m∠CMD + m∠DME = m∠FME + m∠DME | ? |

7. m∠CME = m∠DMF | ? |

8. ∠CME ≅ ∠DMF | ? |

Which of the following is the best reason for statement 6?

*CME*and ∠

*DMF*are congruent.

Statements | Reasons |

1. ∠CMD ≅ ∠AMB | Given |

2. ∠AMB and ∠FME are vertical angles | Given |

3. ∠AMB ≅ ∠FME | ? |

4. ∠CMD ≅ ∠FME | ? |

5. m∠CMD = m∠FME | ? |

6. m∠CMD + m∠DME = m∠FME + m∠DME | ? |

7. m∠CME = m∠DMF | ? |

8. ∠CME ≅ ∠DMF | ? |

Which of the following is the best reason for statement 7?

*CME*and ∠

*DMF*are congruent.

Statements | Reasons |

1. ∠CMD ≅ ∠AMB | Given |

2. ∠AMB and ∠FME are vertical angles | Given |

3. ∠AMB ≅ ∠FME | ? |

4. ∠CMD ≅ ∠FME | ? |

5. m∠CMD = m∠FME | ? |

6. m∠CMD + m∠DME = m∠FME + m∠DME | ? |

7. m∠CME = m∠DMF | ? |

8. ∠CME ≅ ∠DMF | ? |

Which of the following is the best reason for statement 8?