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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14
![**Transcription for Educational Website:**
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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. \(1, -2, 3, -4, \ldots\)
2. \(0, 2, 0, 2, \ldots\)
3. \(Z, Y, X, W, \ldots\)
4. \(A, D, G, J, \ldots\)
![Geometric Shapes]
5. (Picture of a pentagon)
6. (Picture of a cube building)
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.
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 \(\triangle MNT\) into two line segments. So, the line is a segment bisector of \(\triangle MNT\).
In Exercises 15–18, use the Law of Detachment to conclude what you can conclude from the given true statements, if possible. (*See Example 4.*)
15. If you download a GIF, then your device crashes. You downloaded a GIF.
16. If a quadrilateral is a square, then it has four right angles. Quadrilateral \(QRST\) has four right angles.
17. 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 19–22, use the Law of Syllogism to write a new conditional statement that follows from the pair of true](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F190d6977-2ae2-4a51-aa5b-fbc1e2d73150%2F92666f25-f5cd-46be-8dba-167e2b72d161%2Fmvy5kjs_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Transcription for Educational Website:**
---
In Exercises 1–6, describe the pattern. Then write or draw the next two numbers, letters, or figures. (*See Example 1.*)
1. \(1, -2, 3, -4, \ldots\)
2. \(0, 2, 0, 2, \ldots\)
3. \(Z, Y, X, W, \ldots\)
4. \(A, D, G, J, \ldots\)
![Geometric Shapes]
5. (Picture of a pentagon)
6. (Picture of a cube building)
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.
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 \(\triangle MNT\) into two line segments. So, the line is a segment bisector of \(\triangle MNT\).
In Exercises 15–18, use the Law of Detachment to conclude what you can conclude from the given true statements, if possible. (*See Example 4.*)
15. If you download a GIF, then your device crashes. You downloaded a GIF.
16. If a quadrilateral is a square, then it has four right angles. Quadrilateral \(QRST\) has four right angles.
17. 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 19–22, use the Law of Syllogism to write a new conditional statement that follows from the pair of true
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