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. What property of equality would you use to solve for x in the equation 5x = 15?
Symmetry
Transitivity
Substitution
Division
Reflexive
Q. Which is an example of the symmetric property of equality?
A = A
If A = B and B = C, then A = C
If A = B, then B = A
If A = B, B can be used for all A
None of the above
Q. Which of these is not a property of equality (and therefore congruence)?
Symmetry
Reflexivity
Transitivity
Substitution
Inversion
Q. Which property lets us simplify the equation (10 – 5)2x – (10 – 5) = 0 to 52x – 5 = 0?
Transitive Property
Addition Property
Subtraction Property
Reflexive Property
Substitution Property
Q. We are given that A = B and C = D. What would make the statement A/C = B/D untrue?
A = 0
B = C
C = D
D = 0
Nothing, that statement is always true
Q. Fill in the missing statements in the following proof that if 2x + 7 = 1 and y⁄x – 1 = 2, then y = -9.
| Statements | Reasons |
| 1. 2x + 7 = 1 | Given |
| 2. y⁄x – 1 = 2 | Given |
| 3. ? | Subtract 7 from both sides of (1) |
| 4. ? | Divide (3) by 2 |
| 5. ? | Substitute (4) into (2) |
| 6. ? | Add 1 to both sides of (5) |
| 7. ? | Multiply (6) by –3 |
Which of the following fits best for statement 3?
2x = 7
2x = 8
2x + 1 = 7
2x = -6
2x = -8
Q. Fill in the missing statements in the following proof that if 2x + 7 = 1 and y⁄x – 1 = 2, then y = -9.
| Statements | Reasons |
| 1. 2x + 7 = 1 | Given |
| 2. y⁄x – 1 = 2 | Given |
| 3. ? | Subtract 7 from both sides of (1) |
| 4. ? | Divide (3) by 2 |
| 5. ? | Substitute (4) into (2) |
| 6. ? | Add 1 to both sides of (5) |
| 7. ? | Multiply (6) by –3 |
Which of the following fits best for statement 4?
x = 3
x = -3
x = 6
x = -6
x = 4
Q. Fill in the missing statements in the following proof that if 2x + 7 = 1 and y⁄x – 1 = 2, then y = -9.
| Statements | Reasons |
| 1. 2x + 7 = 1 | Given |
| 2. y⁄x – 1 = 2 | Given |
| 3. ? | Subtract 7 from both sides of (1) |
| 4. ? | Divide (3) by 2 |
| 5. ? | Substitute (4) into (2) |
| 6. ? | Add 1 to both sides of (5) |
| 7. ? | Multiply (6) by –3 |
Which of the following fits best for statement 5?
Q. Fill in the missing statements in the following proof that if 2x + 7 = 1 and y⁄x – 1 = 2, then y = -9.
| Statements | Reasons |
| 1. 2x + 7 = 1 | Given |
| 2. y⁄x – 1 = 2 | Given |
| 3. ? | Subtract 7 from both sides of (1) |
| 4. ? | Divide (3) by 2 |
| 5. ? | Substitute (4) into (2) |
| 6. ? | Add 1 to both sides of (5) |
| 7. ? | Multiply (6) by –3 |
Which of the following fits best for statement 6?
Q. Fill in the missing statements in the following proof that if 2x + 7 = 1 and y⁄x – 1 = 2, then y = -9.
| Statements | Reasons |
| 1. 2x + 7 = 1 | Given |
| 2. y⁄x – 1 = 2 | Given |
| 3. ? | Subtract 7 from both sides of (1) |
| 4. ? | Divide (3) by 2 |
| 5. ? | Substitute (4) into (2) |
| 6. ? | Add 1 to both sides of (5) |
| 7. ? | Multiply (6) by –3 |
Which of the following fits best for statement 7?
x = 6
y = 9
y = -9
x = -6
x = -9