# Logic and Proof: Provin' and Groovin' True or False

1. When can you assume angles are vertical in a diagram? -> When they are opposite angles formed by intersecting lines or segments
2. Which is a pair of vertical angles?

-> ∠AOB and ∠WOX

3. 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
4. Which is always true of complementary angles ∠X and ∠Y? -> m∠X + m∠Y = 90
5. 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

6. 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? -> Transitive property of congruence

7. 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? -> Addition property of equality

8. 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? -> Division property of equality

9. 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

10. 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? -> Angle addition postulate