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?
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
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