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

• #32. If , 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