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# Logic and Proof: Provin' and Groovin' Quiz

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
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
Division 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
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