# Logic and Proof: Equality and Congruence for All! True or False

1. What property of equality would you use to solve for x in the equation 5x = 15? -> Symmetry
2. Which is an example of the symmetric property of equality? -> If A = B and B = C, then A = C
3. Which of these is not a property of equality (and therefore congruence)? -> Transitivity
4. Which property lets us simplify the equation (10 – 5)2x – (10 – 5) = 0 to 52x – 5 = 0? -> Reflexive Property
5. We are given that A = B and C = D. What would make the statement A/C = B/D untrue? -> D = 0
6. 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 = -6

7. 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

8. 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? ->

9. 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? ->

10. 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 = -9