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In Exercises 27 and 28, use inductive reasoning to make a conjecture about the given quantity. Then use deductive reasoning to show that the conjecture is true. (See Example 6.) 27. the sum of two add integers

In Exercises 27 and 28, use inductive reasoning to make a conjecture about the given quantity. Then use deductive reasoning to show that the conjecture is true. (See Example 6.) 27. the sum of two add integers

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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In Exercises 1-6, describe the pattern. Then write or draw the next two numbers, letters, or figures. (See Example 1.) 1. 1.-2.3, -4,5.... 3. Z, Y. X, W, V,... ▶5. 6. 2. 0. 2, 6, 12, 20,... 4. A. D. G. J, M, ….. In Exercises 7-10), make and test a conjecture about the given quantity. (See Example 2.) 7. the sum of an even integer and an odd integer 8. the product of any two even integers 9. the quotient of a number and its reciprocal 10. the quotient of two negative integers In Exercises 11-14, find a counterexample to show that the conjecture is false. (See Example 3.) 11. The product of two positive numbers is always greater than either number. x+1 71 12. If n is a nonzero integer, then is always greater than 1. 13. If two angles are supplements of each other, then one of the angles must be acute. 14. A line s divides MN into two line segments. So, the line s is a segment bisector of MN. In Exercises 15-18, use the Law of Detachment to determine what you can conclude from the given information, if possible. (See Example 4.) 15. If you download a GIF, then your device crashes. You download a GIF. 16. If your cousin lets you borrow a car, then you will go to the mountains with your friend. You will go to the mountains with your friend. 17. If a quadrilateral is a square, then it has four right angles. Quadrilateral QRST has four right angles. 18. If a point divides a line segment into two congruent line segments, then the point is a midpoint, Point P divides L.H into two congruent line segments. In Exercises 19-22, use the Law of Syllogism to write a new conditional statement that follows from the pair of true statements, if possible. (See Example 5.) 19. Ifx-2, then |x|> 2. If x > 2, then |x|> 2. 20. If a = 3, then 5o = 15. If / 2 = 1, then a = 3. 21. If a figure is a rhombus, then the figure is a parallelogram. If a figure is a parallelogram, then the figure has two pairs of opposite sides that are parallel. 22. If a figure is a square, then the figure has four congruent sides. If a figure is a square, then the figure has four right angles. In Exercises 23-26, state the law of logic that is illustrated. 23. If you do your homework, then you can watch TV. If you watch TV, then you can watch your favorite show. If you do your homework, then you can watch your favorite show. 24. If you miss practice the day before a game, then you will not be a starting player in the game. You miss practice on Tuesday. You will not start the game Wednesday. 25. Ifx> 12, then x +9> 20. The value of x is 14. So.x+9> 20. 26. If I and 2 are vertical angles, then Z1 = 22. If 41 = 22. then mx21 = m22. If 21 and 22 are vertical angles, then m1 = 22. In Exercises 27 and 28, use inductive reasoning to make a conjecture about the given quantity. Then use deductive reasoning to show that the conjecture is true. (See Example 6.) 27. the sum of two add integers 28. the product of two odd integers GO DIGITAL
Transcribed Image Text:In Exercises 1-6, describe the pattern. Then write or draw the next two numbers, letters, or figures. (See Example 1.) 1. 1.-2.3, -4,5.... 3. Z, Y. X, W, V,... ▶5. 6. 2. 0. 2, 6, 12, 20,... 4. A. D. G. J, M, ….. In Exercises 7-10), make and test a conjecture about the given quantity. (See Example 2.) 7. the sum of an even integer and an odd integer 8. the product of any two even integers 9. the quotient of a number and its reciprocal 10. the quotient of two negative integers In Exercises 11-14, find a counterexample to show that the conjecture is false. (See Example 3.) 11. The product of two positive numbers is always greater than either number. x+1 71 12. If n is a nonzero integer, then is always greater than 1. 13. If two angles are supplements of each other, then one of the angles must be acute. 14. A line s divides MN into two line segments. So, the line s is a segment bisector of MN. In Exercises 15-18, use the Law of Detachment to determine what you can conclude from the given information, if possible. (See Example 4.) 15. If you download a GIF, then your device crashes. You download a GIF. 16. If your cousin lets you borrow a car, then you will go to the mountains with your friend. You will go to the mountains with your friend. 17. If a quadrilateral is a square, then it has four right angles. Quadrilateral QRST has four right angles. 18. If a point divides a line segment into two congruent line segments, then the point is a midpoint, Point P divides L.H into two congruent line segments. In Exercises 19-22, use the Law of Syllogism to write a new conditional statement that follows from the pair of true statements, if possible. (See Example 5.) 19. Ifx-2, then |x|> 2. If x > 2, then |x|> 2. 20. If a = 3, then 5o = 15. If / 2 = 1, then a = 3. 21. If a figure is a rhombus, then the figure is a parallelogram. If a figure is a parallelogram, then the figure has two pairs of opposite sides that are parallel. 22. If a figure is a square, then the figure has four congruent sides. If a figure is a square, then the figure has four right angles. In Exercises 23-26, state the law of logic that is illustrated. 23. If you do your homework, then you can watch TV. If you watch TV, then you can watch your favorite show. If you do your homework, then you can watch your favorite show. 24. If you miss practice the day before a game, then you will not be a starting player in the game. You miss practice on Tuesday. You will not start the game Wednesday. 25. Ifx> 12, then x +9> 20. The value of x is 14. So.x+9> 20. 26. If I and 2 are vertical angles, then Z1 = 22. If 41 = 22. then mx21 = m22. If 21 and 22 are vertical angles, then m1 = 22. In Exercises 27 and 28, use inductive reasoning to make a conjecture about the given quantity. Then use deductive reasoning to show that the conjecture is true. (See Example 6.) 27. the sum of two add integers 28. the product of two odd integers GO DIGITAL
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