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Logic and Proof

Logic and Proof

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.

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?Reflexive 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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