# Logic and Proof: Equality and Congruence for All! Quiz

*? Put your knowledge to the test. Good luck — the Stickman is counting on you!*

**Logic and Proof***x*in the equation 5

*x*= 15?

*A*=

*A*

*A*=

*B*and

*B*=

*C*, then

*A*=

*C*

*A*=

*B*, then

*B*=

*A*

*A*=

*B*,

*B*can be used for all

*A*

^{2x}– (10 – 5) = 0 to 5

^{2x}– 5 = 0?

*A*=

*B*and

*C*=

*D*. What would make the statement

^{A}/

_{C}=

^{B}/

_{D}untrue?

*A*= 0

*B*=

*C*

*C*=

*D*

*D*= 0

*x*+ 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?

*x*= 7

*x*= 8

*x*+ 1 = 7

*x*= -6

*x*= -8

*x*+ 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

*x*+ 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?

*x*+ 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?

*x*+ 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