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Geometry and Logic Questions

Solve geometry problems and logical statements, including angle congruence and system equations. Understand contrapositive and inverse statements. Determine line parallelism and angle properties. Also, explore logical sequences and animal classification.

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Geometry and Logic Questions

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  1. If I get a 100%, then I will have an A. I get a 100% What is q? What is p? I will have an A What is the converse? If I have an A, then I got a 100%.

  2. Solve the system: x + y = 1 x – y = 9 x + y = 1 5 + y = 1 y = -4 2x = 10 x = 5

  3. How do you know that: 1 2 3 4 8 7 6 5 The lines are parallel? Given (labeled in diagram) Angle 8 congruent to angle 2? Vertical angle thm Angle 7 congruent to angle 3? // lines  alt int angles are congruent

  4. JAM is obtuse. Find the restrictions on x. J (6x + 12) M 90 < 6x + 12 < 180 78 < 6x < 168 13 < x < 28 A

  5. Solve the system: 3x + 2y = 15 4x – 6y = 46 9x + 6y = 45 4x – 6y = 46 3x + 2y = 15 3(7) + 2y = 15 21 + 2y = 15 2y = -6 y = -3 13x = 91 x = 7 Multiply by 3

  6. How do you know that: 1 2 3 4 8 7 6 5 Angle 1 congruent to angle 5? // lines  alt ext angles congruent Angle 3 congruent to angle 5? Vertical angle thm Angle 1 congruent to angle 3? // lines  corresponding angles are congruent

  7. If I get a 100%, then I will have an A. If I don’t get a 100%, then I won’t have an A. What is the contrapositive? What is the inverse? If I don’t have an A, then I didn’t get a 100% Is the inverse true or false? False, I could get a 98% and still have an A.

  8. Are the lines // if: (and how do you know?) 1 2 3 4 8 7 6 5 Angle 1 congruent to angle 5? Yes, alt ext angles congruent// lines Angle 3 congruent to angle 5? No Angle 1 congruent to angle 3? Yes, corresponding angles are congruent// lines

  9. GWM is acute. Find the restrictions on x. G (5x – 20) M 0 < 5x – 20 < 90 20< 5x < 110 4< x < 22 W

  10. How do you know that: 1 2 3 4 8 7 6 5 Angle 1 supp to angle 2? Definition of linear pair Angle 1 supp to angle 4? // lines  SSE angles are supp Angle 7 supp to angle 6? // lines  SSI angles are supp

  11. List all pairs of: 1 2 3 4 8 7 6 5 2 & 6, 7 & 3 Alt int angles Corresponding angles 2 & 4, 7 & 5, 8 & 6, 1 & 3 Same Side Interior angles 2 & 3, 7 & 6 Same Side Exterior angles 1 & 4, 8 & 5 Alt ext angles 1 & 5, 8 & 4

  12. Are the lines // if: (and how do you know?) 1 2 3 4 8 7 6 5 Angle 7 congruent to angle 3? Yes, alt int angles congruent// lines Angle 5 supp to angle 6? No Angle 7 supp to angle 6? Yes, SSI angles are supp// lines

  13. If an animal is a zebra, then it is mammal. If an animal is NOT a zebra, then it is not a mammal. What is the contrapositive? What is the inverse? If an animal is not a mammal, then it is not a zebra. Is the inverse true or false? False, the mammal could be a human.

  14. If an animal is a zebra, then it is mammal. An animal is a zebra What is q? What is p? It is a mammal What is the converse? If an animal is a mammal, then it is a zebra.

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