11. The product of two positive numbers is always greater than either number. 12. Il n is a nonzero integer, then is always greater than 1. x + 1 71 13. If two angles are supplements of each other, then one of the angles must be acute. 24. 25.
11. The product of two positive numbers is always greater than either number. 12. Il n is a nonzero integer, then is always greater than 1. x + 1 71 13. If two angles are supplements of each other, then one of the angles must be acute. 24. 25.
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
Related questions
Question
12
![**In Exercises 1–6, describe the pattern. Then write or draw the next two numbers, letters, or figures.**
1. \(1, -2, 3, -4, 5, \ldots\)
2. \(0, 2, 0, 2, 0, \ldots\)
3. \(Z, Y, X, W, V, \ldots\)
4. \(A, D, G, J, M, \ldots\)
5. ![Image showing a sequence of geometric shapes: a triangle, a square, and a pentagon with increasing sides in sequence.]
6. ![Image showing a series of cube arrangements increasing in number: a single cube, a larger cube made of smaller cubes, and so on.]
**In Exercises 7–10, make and test a conjecture about the given quantity.**
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.**
11. The product of two positive numbers is always greater than either number.
12. If \( n \) is a nonzero integer, then \( \frac{n+1}{n} \) 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 \( l \) divides \(\triangle MN \) into two line segments. So, the line is a segment bisector of \(\triangle MN \).
**In Exercises 15–18, use the Law of Detachment to determine what you can conclude from the given true statements.**
15. If you download a GIF, then your device crashes. You download a GIF.
16. If you are not on time, then you are going to be detained. You are not on time.
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 \(\overline{FH}\) into two congruent line segments.
**In Exercises](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F190d6977-2ae2-4a51-aa5b-fbc1e2d73150%2F5a5a7d4d-2af2-400e-9eb6-4e6c860d9edb%2Fxbwsbkn_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**In Exercises 1–6, describe the pattern. Then write or draw the next two numbers, letters, or figures.**
1. \(1, -2, 3, -4, 5, \ldots\)
2. \(0, 2, 0, 2, 0, \ldots\)
3. \(Z, Y, X, W, V, \ldots\)
4. \(A, D, G, J, M, \ldots\)
5. ![Image showing a sequence of geometric shapes: a triangle, a square, and a pentagon with increasing sides in sequence.]
6. ![Image showing a series of cube arrangements increasing in number: a single cube, a larger cube made of smaller cubes, and so on.]
**In Exercises 7–10, make and test a conjecture about the given quantity.**
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.**
11. The product of two positive numbers is always greater than either number.
12. If \( n \) is a nonzero integer, then \( \frac{n+1}{n} \) 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 \( l \) divides \(\triangle MN \) into two line segments. So, the line is a segment bisector of \(\triangle MN \).
**In Exercises 15–18, use the Law of Detachment to determine what you can conclude from the given true statements.**
15. If you download a GIF, then your device crashes. You download a GIF.
16. If you are not on time, then you are going to be detained. You are not on time.
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 \(\overline{FH}\) into two congruent line segments.
**In Exercises
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