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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. Ifx > 2, then x > 2.

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. Ifx > 2, then x > 2.

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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# Educational Content Transcription ## Exercises 1-6 **Describe the Pattern. Then Write or Draw the Next Two Numbers, Letters, or Figures.** 1. Sequence: 1, –2, 3, –4, 5, ... 2. Sequence: 0, 2, 6, 12, 20, ... 3. Sequence: Z, Y, X, W, V, ... 4. Sequence: A, D, G, J, M, ... 5. Diagram: A sequence of polygons (triangle, square). 6. Diagram: A sequence of stacked cubes forming steps. ## 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. ## 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 divides \( \triangle MN \) into two line segments. So, the line is a segment bisector of \( \triangle MN \). ## Exercises 15-18 **Use the Law of Detachment to Conclude What Can Be Concluded from the Given Information.** 15. If you download a GIF, then your device crashes. You download 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 \( \overline{HF} \) into two congruent line segments. ## Exercises 19-22 **Use the Law of Syllogism to Write a New Conditional Statement That Follows from the Pair of True Statements, if Possible.** 19. If \( x < -2 \), then \( |x| > 2 \). If \( x > 2 \), then \( |x| > 2 \).
Transcribed Image Text:# Educational Content Transcription ## Exercises 1-6 **Describe the Pattern. Then Write or Draw the Next Two Numbers, Letters, or Figures.** 1. Sequence: 1, –2, 3, –4, 5, ... 2. Sequence: 0, 2, 6, 12, 20, ... 3. Sequence: Z, Y, X, W, V, ... 4. Sequence: A, D, G, J, M, ... 5. Diagram: A sequence of polygons (triangle, square). 6. Diagram: A sequence of stacked cubes forming steps. ## 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. ## 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 divides \( \triangle MN \) into two line segments. So, the line is a segment bisector of \( \triangle MN \). ## Exercises 15-18 **Use the Law of Detachment to Conclude What Can Be Concluded from the Given Information.** 15. If you download a GIF, then your device crashes. You download 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 \( \overline{HF} \) into two congruent line segments. ## Exercises 19-22 **Use the Law of Syllogism to Write a New Conditional Statement That Follows from the Pair of True Statements, if Possible.** 19. If \( x < -2 \), then \( |x| > 2 \). If \( x > 2 \), then \( |x| > 2 \).
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