Think you’ve got your head wrapped around **Logic and Proof**? Put your knowledge to
the test. Good luck — the Stickman is counting on you!

Q. When can you assume angles are vertical in a diagram?

Only when they are marked as congruent

When they are opposite angles formed by intersecting lines or segments

When they are adjacent angles formed by intersecting lines or segments

When they are not horizontal

When they are complementary

Q. Which is a pair of vertical angles?

∠*COD* and ∠*COB*

∠*AOB* and ∠*WOX*

∠*BOC* and ∠*DOZ*

∠*WOX* and ∠*DOC*

∠*BOA* and ∠*XOY*

Q. In order use the segment addition postulate to conclude that *XY* + *YZ* = *XZ*, what must we know about points *X*, *Y*, and *Z*?

∠*XYZ* and ∠*YZX* are complementary

Q. Which is always true of complementary angles ∠*X* and ∠*Y*?

m∠*X* ≠ m∠*Y*

∠*X* = 180 – m∠*Y*

∠*X* ≅ ∠*Y*

m∠*X* – m∠Y = 90

m∠X + m∠*Y* = 90

Q. Using the figure below, prove that ∠*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?

Definition of angle bisector

Symmetric property of congruence

Vertical angles are congruent

Transitive property of congruence

Definition of congruence

Q. Using the figure below, prove that ∠*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?

Definition of angle bisector

Symmetric property of congruence

Vertical angles are congruent

Reflexive property of congruence

Transitive property of congruence

Q. Using the figure below, prove that ∠*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?

Definition of congruence

Definition of angle bisector

Angle addition postulate

Addition property of equality

Substitution property of equality

Q. Using the figure below, prove that ∠*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?

Definition of congruence

Definition of angle bisector

Angle addition postulate

Division property of equality

Addition property of equality

Q. Using the figure below, prove that ∠*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?

Definition of congruence

Definition of angle bisector

Angle addition postulate

Segment addition postulate

Addition property of equality

Q. Using the figure below, prove that ∠*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?

Definition of congruence

Definition of angle bisector

Angle addition postulate

Addition property of equality

Transitive property of congruence