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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.

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.

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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Question
22
**Educational Website Transcription and Explanation** --- **In Exercises 1–6, describe the pattern. Then write or draw the next two numbers, letters, or figures.** 1. **1, -2, 3, -4, 5, …** Describe and extend the alternating sign pattern. 2. **0, 2, 6, 12, 20, …** Identify the quadratic sequence pattern. 3. **Y, X, W, V, …** Recognize the reverse alphabetical sequence. 4. **A, D, G, J, M, …** Identify the alphabetical sequence with increments of three. 5. **Figures (squares, then triangle, hexagon, …)** Identify the pattern of increasing polygon sides. 6. **Cubes Arrangement** Extend the spatial pattern based on the given 3D arrangement. --- **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 \( n + \frac{1}{n} \) 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 \(\overline{MN}\) into two line segments. So, the line is a segment bisector of \(\overline{MN}\). --- **In Exercises 15–18, use the Law of Detachment to determine what you can conclude from the given information.** 15. If you download a GIF, then your device crashes. You download a GIF. 16. If you do your homework, then you will go on the field trip. You will go to the field trip. 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
Transcribed Image Text:**Educational Website Transcription and Explanation** --- **In Exercises 1–6, describe the pattern. Then write or draw the next two numbers, letters, or figures.** 1. **1, -2, 3, -4, 5, …** Describe and extend the alternating sign pattern. 2. **0, 2, 6, 12, 20, …** Identify the quadratic sequence pattern. 3. **Y, X, W, V, …** Recognize the reverse alphabetical sequence. 4. **A, D, G, J, M, …** Identify the alphabetical sequence with increments of three. 5. **Figures (squares, then triangle, hexagon, …)** Identify the pattern of increasing polygon sides. 6. **Cubes Arrangement** Extend the spatial pattern based on the given 3D arrangement. --- **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 \( n + \frac{1}{n} \) 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 \(\overline{MN}\) into two line segments. So, the line is a segment bisector of \(\overline{MN}\). --- **In Exercises 15–18, use the Law of Detachment to determine what you can conclude from the given information.** 15. If you download a GIF, then your device crashes. You download a GIF. 16. If you do your homework, then you will go on the field trip. You will go to the field trip. 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
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