Name———————————————————————— Lesson 2.1 Date ————————————— Practice A For use with the lesson “Use Inductive Reasoning” Sketch the next figure in the pattern. 1. 3. 2. 4. 5. Lesson 2.1 6. Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved. 7. The first four objects in a pattern are shown. How many squares are there in the next object? 8. 9. Geometry Chapter Resource Book CS10_CC_G_MECR710761_C2L01PA.indd 7 2-7 4/27/11 3:25:06 PM Name———————————————————————— Date ————————————— Practice A continued Lesson 2.1 For use with the lesson “Use Inductive Reasoning” Describe a pattern in the numbers. Write the next number in the pattern. 10. 5, 10, 15, 20, . . . 11. 26, 23, 20, 17, 14, . . . 12. 2, 6, 18, 54, . . . 13. 32, 16, 8, 4, . . . 14. 212, 28, 24, 0, . . . 15. 3, 29, 27, 281, . . . Complete the conjecture based on the pattern you observe in the specific cases. 16. Use the following products of odd integers to complete the conjecture about the Conjecture The product of any two odd integers is ? . 17. Complete the following table. Then complete the conjecture that follows. Pair of odd numbers 1, 3 Sum of the numbers divided by 2 3, 5 113 2 7, 9 9, 11 315 } Average of numbers 5, 7 } 2 2 Conjecture The average of any two consecutive odd whole numbers is ? . Show the conjecture is false by finding a counterexample. 18. The average of any two consecutive even numbers is an even number. 19. Any four-sided polygon is a square. 20. The square of any integer is a positive integer. 21. Evaporation You are performing an experiment to explore the effects of surface area on evaporation. Each day you record the depth (in millimeters) of the water in the bowl pictured. The table below shows your results. Day Water level (mm) 0 1 2 3 4 5 180 169 158 147 136 125 a. Predict the height of the water surface in the bowl on day 6. b. Based on these results, make a conjecture about how the surface area of a body of water affects the rate of change of its depth by evaporation. 2-8 Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved. Lesson 2.1 product of any two odd numbers: 1 3 3 5 3, 1 3 5 5 5, 3 3 3 5 9, 3 3 5 5 15, 5 3 1 5 5, 5 3 5 5 25, 5 3 7 5 35, 7 3 1 5 7, 7 3 3 5 21, 7 3 7 5 49 Geometry Chapter Resource Book CS10_CC_G_MECR710761_C2L01PA.indd 8 4/27/11 3:25:06 PM Answers for Chapter 2 Lesson 2.1 Use Inductive Reasoning Teaching Guide front and a 0 between the 8 and 1; 99,980,001; 9,999,800,001 2. 111,105; 222,210; 333,315; Pattern: the first three numbers are a multiple of 111 and the last three numbers are a multiple of 105. Increase both by one multiple each time; 444,420; 555,525 3. 9; 1089, 110,889; (Pattern: a 1 is placed at the beginning of the number and an extra 8 is placed in front of the 9); 11,108,889; 1,111,088,889 21. a. 114 mm b. conjecture: The rate of change of depth of a body of water is not affected by the surface area. Practice Level B 1. 2. 113 224 100 200 0 2. 3 3. Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved. 5. 300 557 400 9 6 13 500 18 600 24 9 12 15 18 21 24 27 30 1 3 6. 8. 9 9. 15 7. 446 7. add 2 to the numerator and 1 to the 9 denominator; } 7 0.0 4. 335 6. add consecutive integers to each term, starting with 2; 24 4 6 Practice Level A 1. 4. 5. add 111 to each term; 557 Technology Activity 1. about 25.68 3. answers 1. 81; 9801; 998,001; Pattern: place a 9 in Reasoning and Proof 0.2 3 4 0.4 0.6 5 5 0.8 7 6 1.0 9 7 1.2 1.4 8. subtract 1 from the numerator and 1 from the 3 denominator; }4 0.70 3 4 4 5 5 6 0.75 0.80 6 7 7 8 0.85 0.90 0.95 9. subtract 3 from each term; 29 10. add 5 to previous term; 25 11. subtract 3 from previous term; 11 12. multiply previous term by 3; 162 13. divide previous term by 2; 2 14. add 4 to previous term; 4 15. multiply previous term by 23; 243 16. an odd integer 17. 3, 5 5, 7 7, 9 9, 11 315 517 719 9 1 11 4 6 8 10 } } 2 } 2 } 2 2 29 26 210 28 26 0 23 24 22 3 0 2 4 10. square numbers; 25 1 0 4 3 9 6 16 25 9 12 15 18 21 24 27 30 11. double the number and add 1; 47 2 5 0 11 23 47 5 10 15 20 25 30 35 40 45 50 12. prime numbers; 13 1 2 3 5 7 3 5 7 9 11 13 11 13 15 the even number between the consecutive odd numbers. 2 13. 16 14. 20 15. Sample answer: } 5 0.5 4 214 18. Sample answer: } 5 3, 3 is not even. 2 16. Sample answer: 5 2 7 5 22 19. Sample answer: is not a square. 20. Sample answer: 02 is not a positive integer. 22 17. Sample answer: } 52 22 1 1 Î } 1 1 1 1 18. Sample answer: } 5 } 2 , } 2 > } 4 4 Geometry Chapter Resource Book CS10_CC_G_MECR710761_C2AK.indd 13 A13 4/27/11 6:42:27 PM

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