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Geometry – Review of Properties

Geometry – Review of Properties. #1. If 2x + 1 = 13, then 2x = 12 Subtraction  #2. If 2x + 1 = 13, then x = 6 Subtraction AND Division #3. If x – 19 = 6, then x = 25 . Addition #4. If 6x + 7x – 9 = 14, then 13x – 9 = 14 . CLT # 5. If 2(x – 1) = 18, then 2x – 2 = 18 .

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Geometry – Review of Properties

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  1. Geometry – Review of Properties

  2. #1. If 2x + 1 = 13, then 2x = 12 • Subtraction  • #2. If 2x + 1 = 13, then x = 6 • Subtraction AND Division • #3. If x – 19 = 6, then x = 25. • Addition • #4. If 6x + 7x – 9 = 14, then 13x – 9 = 14. • CLT • #5. If 2(x – 1) = 18, then 2x – 2 = 18. • Distributive Property • #6. m<7 = m<7 • Reflexive property

  3. #7. If m<7 = 2x + 1 and 2x + 1 = m<9, then m<7 = m<9. • Trans • #8. If x = 9 and 9 = z, then x = z. • Trans • #9. If 4x + 17 = b and a + 1 = b, then 4x + 17 = a + 1 • Trans • #10. If <5 = x + z and x = 6, then <5 = 6 + z. • Sub • #11. If <6 + <9 = 180, then <6 & <9 are supplementary • Converse of DefSupp

  4. Use the figure for the next SIX questions: • #12. <3 + <4 = <COF. • Angle Add Post • #13. <COF is a right angle. • Def Right Angle • #14. If <COF = 90, then <COF is a right angle. • Converse of Def Right Angle • #15. <COA and <COF are a linear pair. • Def Linear pair • #16. If <COA and <COF are a linear pair, then <COA and <COF are supplementary. • Linear Pair Postulate • #17. <2 + <3 = <BOD • Angle Addition Postulate

  5. #18. If 5x + 1 = 17, then 17 = 5x + 1 • Symmetric • #19. t + v = v + t • Commutative Property for addition • #20. <ABC = <ABC. • Reflexive • #21. a + (x + w) = (a + x) + w • Associative Property for Addition • #22. If <1 = 174 degrees, then <1 is an obtuse angle. • Converse of Def Obtuse Angle

  6. Use the figure for the next SIX questions. • #23. DE + EF = DF • Segment Addition Postulate • #24. If DE + EF = DF, then 3x + 5 + 5x – 13 = 24. • Sub • #25. If 3x + 5 + 5x – 13 = 24, then 8x – 8 = 24. • CLT • #26. If 8x – 8 = 24, then 8x = 32. • Addition • #27. If 8x = 32, then x = 4. • Division • #28. If x = 4, then EF = 7 • Sub

  7. #29. If <B + <B + <C = 105, then 2<B + <C = 105. • CLT • #30. If 4x + 9 = 90, then 4x = 81. • Subtraction • #31. <1 = <1 • Reflexive • #32. If , then b = 28. • Multiplication • #33. If <8 = <10 and <8 = <11, then <11 = <10. • Trans

  8. Use the figure for the next SIX questions: • #34. <AOE and <COD are vertical angles. • Definition of Vertical Angles • #35. If <AOE and <COD are vertical angles, then <AOE = <COD. • Vertical Angle Theorem • #36. <AOC and <COD are a linear pair. • Definition of Linear Pair • #37. <AOC and <COD are supplementary • Linear Pair Postulate • #38. <BOC + <COD = <BOD. • Angle Addition Postulate • #39. If <AOC + <COD = 180, then <AOC and <COD are supplementary. • Converse of Definition of Supplementary

  9. Use the figure for the next TEN questions: • #40. S is the midpoint of RT • Def Midpoint • #41. If S is the midpoint of RT, then RS = ST. • Def Midpoint • #42. If RS = ST, then S is the midpoint of RT. • Converse Def Midpoint • #43. If RS = ½ RT, then S is the midpoint of RT. • Converse Midpoint Theorem • #44. If S is the midpoint of RT, then ST = ½ RT • Midpoint Theorem

  10. #45. RS + ST = RT • Seg Add Post • #46. 6x + 8 + 6x + 8 = 52 • Sub • #47. If 2(6x + 8) = 52, then 12x + 16 = 52. • Distributive Prop • #48. If 12x + 16 = 52, then 12x = 36. • Subtr • #49. If 12x = 36, then x = 3. • Division

  11. #50. If <7= 4x + 9 and <7 = 90, then 4x +9 = 90. • Trans • #51. If 6x + b = 24 and b = 9, then 6x + 9 = 24. • Sub • #52. AB = AB • Reflex • #53. x + 1 = 1 + x • Commutative • #54. If x + 1 = 8, then 8 = x + 1 • Symmetric

  12. #55. If x + 1 = 8 and 8 = d, then x + 1 = d. • Trans • #56. If x + a = 8, and a = 1, then x + 1 = 8. • Sub • #57. If B is a midpoint of AZ, the ZB = ½ AZ. • Midpoint Theorem • #58. If <1 + <17 = 90, then <1 & <17 are complementary angles. • Converse Def Comp

  13. Use the figure for the next SEVEN questions: • #59. If segment AD is perpendicular to ray OB, then <AOB is a right angle. • Def Perpendicular • #60. If <AOB is a right angle, then <AOB = 90. • Def Right Angle • #61. If <AOB = 90, then <AOB is a right angle. • ConvDef Right Angle • #62. If <AOB is a right angle, then segment AD is perpendicular to ray OB. • ConvDefPerp • #63. <AOC and <DOE are vertical angles. • DefVert Angles • #64. If <AOC and <DOE are vertical angles, then <AOC = <DOE. • Vert Angle Theorem • #65. <AOE + <AOC = <EOC. • Angle Add Post

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