More Practice 3.1 PDF
Document Details
Uploaded by SustainableMaxwell
Tags
Summary
This document contains practice problems on geometry concepts like lines, planes, and oblique lines. The problems involve determining if statements are true or false about different geometry relationships and solving systems of linear equations. It is an exercise set focused on geometry.
Full Transcript
Name:____________________________ Date:_________________ Period:__________ More Practice 3.1 Given the right prism, decide if the following statements are TRUE or FALSE. 1. 𝑃𝑙𝑎𝑛𝑒 𝐴𝐸𝐷 ∥ 𝑃𝑙𝑎𝑛𝑒 𝐹𝐺𝐻 _______________________ 2. 𝑃𝑙𝑎𝑛𝑒 𝐴𝐵𝐻 ∥ 𝑃𝑙...
Name:____________________________ Date:_________________ Period:__________ More Practice 3.1 Given the right prism, decide if the following statements are TRUE or FALSE. 1. 𝑃𝑙𝑎𝑛𝑒 𝐴𝐸𝐷 ∥ 𝑃𝑙𝑎𝑛𝑒 𝐹𝐺𝐻 _______________________ 2. 𝑃𝑙𝑎𝑛𝑒 𝐴𝐵𝐻 ∥ 𝑃𝑙𝑎𝑛𝑒 𝐹𝐶𝐷 _______________________ 3. 𝑃𝑙𝑎𝑛𝑒 𝐴𝐵𝐶 ⊥ 𝑃𝑙𝑎𝑛𝑒 𝐽𝐹𝐸 _______________________ 4. 𝑃𝑙𝑎𝑛𝑒 𝐶𝐵𝐻 ⊥ 𝑃𝑙𝑎𝑛𝑒 𝐻𝐼𝐴 _______________________ 5. ⃖4444⃗ 𝐴𝐵 𝑎𝑛𝑑 ⃖4444⃗ 𝐻𝐺 𝑎𝑟𝑒 𝑠𝑘𝑒𝑤 𝑙𝑖𝑛𝑒𝑠._______________________ 6. ⃖444⃗ 𝐶𝐺 𝑎𝑛𝑑 ⃖44⃗ 𝐴𝐼 𝑎𝑟𝑒 𝑠𝑘𝑒𝑤 𝑙𝑖𝑛𝑒𝑠._______________________ 7. ⃖4444⃗ 𝐴𝐸 𝑎𝑛𝑑 ⃖4444⃗ 𝐵𝐶 𝑎𝑟𝑒 𝑠𝑘𝑒𝑤 𝑙𝑖𝑛𝑒𝑠._______________________ 8. ⃖4444⃗ 𝐴𝐵 ∥ ⃖444⃗ 𝐼𝐻 _______________________ 9. ⃖444⃗ ⃖44⃗ 𝑎𝑟𝑒 𝑠𝑘𝑒𝑤 𝑙𝑖𝑛𝑒𝑠. _______________________ 𝐶𝐹 𝑎𝑛𝑑 𝐴𝐽 10. ⃖4444⃗ 𝐴𝐷 ∥ 𝐼𝐹⃖44⃗ _______________________ 11. ⃖4444⃗ 𝐴𝐵 𝑎𝑛𝑑 ⃖4444⃗ 𝐵𝐶 𝑎𝑟𝑒 𝑜𝑏𝑙𝑖𝑞𝑢𝑒 𝑙𝑖𝑛𝑒𝑠._______________________ 12. ⃖4444⃗ 𝐸𝐷 ∥ 𝐼𝐺⃖44⃗ _______________________ 13. ⃖4444⃗ ⃖4⃗ 𝑎𝑟𝑒 𝑜𝑏𝑙𝑖𝑞𝑢𝑒 𝑙𝑖𝑛𝑒𝑠._______________________ 𝐶𝐻 𝑎𝑛𝑑 𝐼𝐽 14. ⃖4444⃗ 𝐴𝐵 ⊥ 𝐴𝐸⃖4444⃗ _______________________ 15. ⃖4444⃗ 𝐴𝐸 𝑎𝑛𝑑 ⃖44⃗ 𝐴𝐽 𝑎𝑟𝑒 𝑜𝑏𝑙𝑖𝑞𝑢𝑒 𝑙𝑖𝑛𝑒𝑠._______________________ 16. ⃖4444⃗ 𝐷𝐹 ⊥ ⃖4444⃗ 𝐷𝐸 _______________________ 17. 𝑃𝑙𝑎𝑛𝑒 𝐶𝐵𝐻 𝑎𝑛𝑑 𝑃𝑙𝑎𝑛𝑒 𝐻𝐼𝐴 𝑎𝑟𝑒 𝑜𝑏𝑙𝑖𝑞𝑢𝑒 𝑝𝑙𝑎𝑛𝑒𝑠. _______________________ 18. 𝑃𝑙𝑎𝑛𝑒 𝐶𝐴𝐹 𝑎𝑛𝑑 𝑃𝑙𝑎𝑛𝑒 𝐺𝐼𝐸 𝑎𝑟𝑒 𝑜𝑏𝑙𝑖𝑞𝑢𝑒 𝑝𝑙𝑎𝑛𝑒𝑠. _______________________ Solve the following systems and describe the lines. 𝑥 + 2𝑦 = 8 2𝑥 + 3𝑦 = 12 19. B _________________ 20. B ___________________ 𝑥 − 2𝑦 = 4 5𝑥 = 3𝑦 − 14 𝑥 + 2𝑦 = 9 2𝑥 + 3𝑦 = 7 21. B _________________ 22. B __________________ 3𝑥 + 2𝑦 = 7 4𝑥 + 6𝑦 = 14 Given the following equations and points, find: a) The equation of a parallel line that passes through the point. b) The equation of a perpendicular line that passes through the point. 23. 𝑦 = 2𝑥 – 5 ( 6, 8 ) a.)_______________________ b.)_______________________ 24. 𝑦 = ¼𝑥 – 3 ( 8, 2 ) a.)_______________________ b.)_______________________ 25. 𝑦 = −3𝑥 + 2 ( −6, 0 ) a.)_______________________ b.)_______________________ 26. 𝑦 = −2 ( 7, 9 ) a.)_______________________ b.)_______________________ 27. 2𝑥 – 𝑦 = 1( −2, 6) a.)_______________________ b.)_______________________ 28. Below is a student’s solution solving a system of equations. Based on their work, what is the correct solution? Circle the letter of your answer. 𝑦 = 2𝑥 + 4 ! Solution 3𝑦 − 6𝑥 = 12 3(𝟐𝒙 + 𝟒) − 6𝑥 = 12 A. (12, 12) B. 𝐼𝑛𝑓𝑖𝑛𝑖𝑡𝑒𝑙𝑦 𝑀𝑎𝑛𝑦 𝑆𝑜𝑙𝑢𝑡𝑖𝑜𝑛𝑠 6𝑥 + 12 − 6𝑥 = 12 C. ∅ (𝑛𝑜 𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛) D. ℝ (𝑎𝑙𝑙 𝑟𝑒𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟𝑠) 12 = 12
