Transcript 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.
– 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 + 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
• #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
𝑏
4
• #32. If = 7, then b = 28.
– Multiplication
• #33. If <8 = <10 and <8 = <11, then <11 = <10.
– Trans
• 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 + 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
• #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