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. – Distributive Property #6. m<7 = m<7 – Reflexive property
#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 Def Supp
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
#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
Use the figure for the next SIX questions. #23. DE + EF = DF – Segment Addition Postulate #24. If DE + EF = DF, then 3x x – 13 = 24. – Sub #25. If 3x x – 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
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
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
#45. RS + ST = RT – Seg Add Post #46. 6x x + 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
#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
#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
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. – Conv Def Right Angle #62. If <AOB is a right angle, then segment AD is perpendicular to ray OB. – Conv Def Perp #63. <AOC and <DOE are vertical angles. – Def Vert Angles #64. If <AOC and <DOE are vertical angles, then <AOC = <DOE. – Vert Angle Theorem #65. <AOE + <AOC = <EOC. – Angle Add Post