# Logic and Proof: Equality and Congruence for All! 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. 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
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 yx – 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 yx – 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 yx – 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 yx – 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 yx – 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