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Mid-Term Review 2014-2015 Use the diagram at the right for Exercises 1β2. 1. Name three collinear and three coplanar points. 2. Name two opposite rays. 3. Μ Μ Μ πΊπΌ bisects β π·πΊπ» so that πβ π·πΊπΌ is π₯ β 3 and πβ πΌπΊπ» is 2π₯ β 13. What is π₯? 4. β 1 and β 2 are supplementary angles. πβ 1 is 4π¦ + 7 and πβ 2 is 9π¦ + 4. What is πβ 2? Μ Μ Μ Μ . Find the coordinates of the midpoint of π¨π© 5. π΄(6, 7), π΅(4, 3) 6. π΄(ο1, 5), π΅(2, ο3) Find the distance between each pair of points. If necessary, round to the nearest tenth. 7. π΄(6, 7), π΅(ο1, 7) 8. πΈ(ο1, 0), πΉ(12, 0) Algebra Use the figure at the right 9. Given: ππ = 3π₯ + 3 and ππ = 2π₯ + 9. a. What is the value of ππ? b. What is the value of ππ? Find a pattern for each sequence. Use the pattern to show the next two terms. 10. 5, 11, 18, 26, β¦ 11. ο3, 6, ο12, 24, ο48, β¦ Identify the hypothesis and conclusion of each conditional. 12. If a number is divisible by 2, then the number is even. Write each sentence as a conditional. 13. Two complementary angles form a right angle. Write the converse, inverse and contrapositive of the given conditional statement. Determine the truth value of all three statements. If a statement is false, give a counterexample. 14. If a figure is a rectangle, then it has exactly four sides. Identify all pairs of each type of angle in the diagram below right. 15. corresponding angles 16. Same-side interior angles 17. alternate interior angles 18. alternate exterior angles Find mο1 and mο2. Justify each answer. 19. 20. Algebra Determine the value of x for which r β s. Then find the measure of each labeled angle. 21. 22. Algebra Find the value of each variable. 23. 24. Find each missing angle measure. 25. 26. Find the slope of the line passing through the given points. 27. (2, 3), (ο1, ο6) 28. (ο6, ο2), (ο3, ο6) Use the given information to write an equation for each line. 29. slope 6, y-intercept 4 30. slope ο 13 , y-intercept ο2 Write each equation in slope-intercept form. 31. π¦ ο 3 = 4(π₯ + 2) 32. π¦ ο 2 = ο2(π₯ ο 5) 33. π¦ + 1 = 1 2 (π₯ + 4) β‘ that contains point C. 34. Write an equation of the line parallel to π¨π© β‘π΄π΅ π¦ = β5π₯ + 12; πΆ( β2, 1) 35. Write an equation of the line perpendicular to the given line that contains P.. π(β6, 5); π¦ = 2π₯ β 3 Algebra Find the values of the variables. 36. 37. State the postulate or theorem (SSS, SAS, ASA, AAS or HL) you can use to prove each pair of triangles congruent. If the triangles cannot be proven congruent, write not enough information. 38. 41. 39. 42. 40. 43. 44. 47. 50. 45. 46. 48. 49. 51. Algebra Find the values of x and y. 53. 52. 54. Algebra Find the value of x. 55. 56. Find the value of x 57. 58. List the angles of each triangle in order from smallest to largest. 59. οπ΄π΅πΆ, where π΄π΅ = 17, π΄πΆ = 13, and π΅πΆ = 29 List the sides of each triangle in order from shortest to longest. 60. οABC, with mοA = 99, mοB = 44, and mοC = 37 Are the following the sides of a triangle. 61. 10ππ, 7ππ, 5ππ 62. 12ππ, 8ππ, 4ππ 63. The length of two sides of triangle are 8cm and 6 cm. Find the range of possible lengths of the third side. Find the range of possible values for each variable. 64. 65.