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Ruler & Protractor Postulates

Ruler & Protractor Postulates. Santucci’s Starter: 1. Complete with sometimes, always, or never: Two lines that lie in parallel planes are ______ parallel. Two lines in intersecting planes are ___________ skew. 2. Explain the difference between skew and parallel lines.

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Ruler & Protractor Postulates

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  1. Ruler & Protractor Postulates Santucci’s Starter: 1. Complete with sometimes, always, or never: Two lines that lie in parallel planes are ______ parallel. Two lines in intersecting planes are ___________ skew. 2. Explain the difference between skew and parallel lines.

  2. Ruler & Protractor Postulates Ruler Postulate Find AB Protractor Postulate

  3. Distance on the x-y plane (1-7) Ex: Find the distance between (3, -4) and (5, 6) in simplified, exact form

  4. Segment Addition Postulate • If A, B, and C are collinear and B is between A & C then AB + BC = AC AC = 60 find x and AB

  5. Angle AdditionPostulate • If <AOC and <COD are adjacent angles, m<AOC + m<COD = m<AOD

  6. EXAMPLE m<AOC = x, m<COD = 5x + 4 and m<AOD = 70 find x and m<COD

  7. GEOMETRY LESSON 1–4 25. 90; right 26. 135; obtuse 27. 34 28. 70 29.Q 30. 6 31. –4 32. 1 33. –2.5, 2.5 34. –3.5, 3.5 35. –6, –1, 1, 6 37–41. Peer edit your work. 55. about 42° 56–58. Answers may vary. Samples are given. 56. 3:00, 9:00 57. 5:00, 7:00 58. 6:00, 12:32 59. 180 60. 150 61. 30 62. 100 63. 40 64. 80 65. 125 66. 125 1-4

  8. M is the midpoint of RT. Find RM, MT, and RT. Midpoints

  9. Try it! If B is between A and C, find the value of x and the measure of BC AB = 3(x + 7) BC = 2(x – 3) AC = 50

  10. Using more algebra If B is between A and C, find the value of x and the measure of BC AB = x2 + 20 BC = 3 - x AC = 17

  11. QN bisects DNB. 1. Construct AC so that ACNB. 2. Construct the perpendicular bisector of AC. 3. Construct RST so that RSTQNB. 4. Construct the bisector of RST. 5. Find x. 6. Find mDNB. Bisectors

  12. Find x if ray WR is an angle bisector • Ray RT bisects <ARF. m<FRT = 2x+10, m<ARF = 8x+4 • Draw a labeled diagram then find x and m<ART. • When done pick up handout & peer edit hw. Starters:

  13. HW Answers p. 32 • 79. 30 • 82. C • 83.F • 84. D • 85.H • 79 and 167 • 87. never • 88. never • 89. always • 90. never • 91. always • 92. always • 93. always • 94. never 70. a. 19.5 b. 43; 137 c.Answers may vary. Sample: The sum of the measures S/B 180. 71.y = 15; AC = 24, DC = 12 72.ED = 10, DB = 10, EB = 20 75. 12; m AOC = 82, m AOB = 32, m BOC = 50 76. 8; m AOB = 30, m BOC = 50, m COD = 30 77. 18; m AOB = 28, m BOC = 52, m AOD = 108 78. 7; m AOB = 28, m BOC = 49, m AOD = 111

  14. HW Answers p. 46 • 25 43. 18. (4, 2) 35. 5.4; (–2.5, 3) 42. ST = (5 – 2)2 + (–3 – (–6))2 = 9 + 9 = 3 2 4.2 TV = (6 – 5)2 + (–6 – (–3))2 = 1 + 9 = 10 3.2 SW = (5 – 6)2 + (–9 – (–6))2 = 9 + 9 = 3 2 4.2 No, but ST = SW and TV = VW. The midpts. Are the same, (5, 4). The diagonals bisect each other.

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