Logic and Proof 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.

StatementsReasons
1. ∠CMD ≅ ∠AMBGiven
2. ∠AMB and ∠FME are vertical anglesGiven
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.

StatementsReasons
1. ∠CMD ≅ ∠AMBGiven
2. ∠AMB and ∠FME are vertical anglesGiven
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.

StatementsReasons
1. ∠CMD ≅ ∠AMBGiven
2. ∠AMB and ∠FME are vertical anglesGiven
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.

StatementsReasons
1. ∠CMD ≅ ∠AMBGiven
2. ∠AMB and ∠FME are vertical anglesGiven
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.

StatementsReasons
1. ∠CMD ≅ ∠AMBGiven
2. ∠AMB and ∠FME are vertical anglesGiven
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.

StatementsReasons
1. ∠CMD ≅ ∠AMBGiven
2. ∠AMB and ∠FME are vertical anglesGiven
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

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