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Geometry Chapter 2 Review: Key Concepts and Important Strategies

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This review resource focuses on fundamental concepts in Geometry Chapter 2, covering conditionals, biconditionals, logic laws, and problem-solving strategies. It includes guidance on how to identify properties like reflexive, symmetric, and distributive, as well as practical examples involving angle measures and segment lengths. Students are encouraged to study definitions, theorems, and postulates in preparation for their test. Effective test-taking strategies and self-assessment advice are also provided to help students perform at their best.

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Geometry Chapter 2 Review: Key Concepts and Important Strategies

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  1. Geometry Chapter 2 Review mbhaub@mpsaz.org

  2. Chapter 2 Review • Work quickly. • Only copy what is necessary. • Use a book or notes for theorems, definitions, postulates, but only when really needed. • All answers on paper. • Keep track of correct & wrong answers. Geometry Chapter 2 Review

  3. Conditionals If today is Friday, then there is a football game. • Write the • Converse • Inverse • Contrapositive If there is a football game, then today is Friday. If today isn’t Friday, then there isn’t a football game. If there isn’t a football game, then today isn’t Friday. Geometry Chapter 2 Review

  4. if and only if x = 25. Biconditionals 4. Rewrite this statement as a conditional and its converse. Geometry Chapter 2 Review

  5. Logic If Mike buys a car, then he will need insurance. Mike buys a car. Conclusion: He needs insurance. 5. What Law makes this a valid argument? Law of Detachment Geometry Chapter 2 Review

  6. Law of Detachment (again) P  Q is true. P is true. Conclusion: Q is true. P  Q P Q Geometry Chapter 2 Review

  7. Logic If you pass the AIMS, then you will graduate. If you graduate, then you can go to college. 6.Use the Law of Syllogism and write a conclusion. If you pass the AIMS, then you can go to college. Geometry Chapter 2 Review

  8. Syllogism (again) If P  Q, and Q  R, then P  R Geometry Chapter 2 Review

  9. Properties 7 – 12: Identify the property used. • 5 =5 • If 5 = x, then x = 5 • 3(x + 6) = 3x + 18 • If x + 3 = 8, then x = 5 • If A  C, then mA = mC • If MN = OP, then reflexive symmetric distributive subtraction def. congruent angles def. congruent segments Geometry Chapter 2 Review

  10. A B C 10x + 8 15x + 12 Problem Solving 38 57 13. If AC = 95, find AB and BC. Solution: (10x + 8) + (15x + 12) = 95 25x + 20 = 95 25x = 75 x = 3 AB = 10(3) + 8 = 38 BC = 15(3) + 12 = 57 Geometry Chapter 2 Review

  11. 1 52° Problem Solving 14. Find m1. 52° Vertical Angles are Congruent Geometry Chapter 2 Review

  12. 1 (5x + 6)° (3x + 20)° Problem Solving 139° 15. Find m1. 41° 5x + 6 = 3x + 20 2x = 14 x = 7 3(7) + 20 = 41 180 – 41 = 139 Geometry Chapter 2 Review

  13. 2 72° Problem Solving 180 – 72 = 16. Find m2. 108° Geometry Chapter 2 Review

  14. (8x + 30)° (2x + 10)° Problem Solving 17. Find the measure of each angle. 142° 38° Angles in a linear pair are supplementary. (8x + 30) + (2x + 10) = 180 10x + 40 = 180 10x = 140 x = 14 8(14) + 30 = 142 2(14) + 10 = 38 Geometry Chapter 2 Review

  15. Distance Formula 18. Find the length of the segment between (8, 6) and (5, 4). Geometry Chapter 2 Review

  16. Midpoint 19. Find the midpoint of the segment between (10, –3) and (20, 17). Geometry Chapter 2 Review

  17. Proof 1 2 20. Given: 2  3 Prove: 1  4 3 4 Statements Reasons You provide these. • 2  3 • 1 supp. 2 • 4 supp. 3 • 1  4 • QED • Given • Linear Pair Post. • Linear Pair Post. •  supps (Th. 2.4) Geometry Chapter 2 Review

  18. How did you do? • Count up the number correct. • 18 – 20: Great work. That’s an A. • 16 – 17: Better than average – B. • 14 – 15: Average – C. • 12 – 13: Below average – D. • 0 – 11: Failing. F. Need to study a lot! Geometry Chapter 2 Review

  19. Homework Then: take time to memorize the definitions, postulates, properties and theorems we’ve seen so far. You really want them in your head by test time. Geometry Chapter 2 Review

  20. Test Tomorrow • Study tonight: know definitions, theorems, postulates. • Get a good night’s rest. • Have a good breakfast or lunch. Eat brain food. • Be on time. • You will only have one period to complete the test. Geometry Chapter 2 Review

  21. Remember… • You may not leave the room unless you are finished with the test. • Any cell phone use – for anything – will result in an automatic zero. Geometry Chapter 2 Review

  22. Goodluck! Geometry Chapter 2 Review

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