Int Math 2 Section 5-6 1011

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Quadrilaterals and Parallelograms

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Int Math 2 Section 5-6 1011

  1. 1. SECTION 5-6 Quadrilaterals and ParallelogramsMon, Jan 31
  2. 2. ESSENTIAL QUESTIONS How do you classify different types of quadrilaterals? What are the properties of parallelograms, and how do you use them? Where you’ll see this: Construction, civil engineering, navigationMon, Jan 31
  3. 3. VOCABULARY 1. Quadrilateral: 2. Parallelogram: 3. Opposite Angles: 4. Consecutive Angles: 5. Opposite Sides: 6. Consecutive Sides:Mon, Jan 31
  4. 4. VOCABULARY 1. Quadrilateral: A four-sided figure 2. Parallelogram: 3. Opposite Angles: 4. Consecutive Angles: 5. Opposite Sides: 6. Consecutive Sides:Mon, Jan 31
  5. 5. VOCABULARY 1. Quadrilateral: A four-sided figure 2. Parallelogram: A quadrilateral with two pairs of parallel sides 3. Opposite Angles: 4. Consecutive Angles: 5. Opposite Sides: 6. Consecutive Sides:Mon, Jan 31
  6. 6. VOCABULARY 1. Quadrilateral: A four-sided figure 2. Parallelogram: A quadrilateral with two pairs of parallel sides 3. Opposite Angles: In a quadrilateral, the angles that do not share sides 4. Consecutive Angles: 5. Opposite Sides: 6. Consecutive Sides:Mon, Jan 31
  7. 7. VOCABULARY 1. Quadrilateral: A four-sided figure 2. Parallelogram: A quadrilateral with two pairs of parallel sides 3. Opposite Angles: In a quadrilateral, the angles that do not share sides 4. Consecutive Angles: Angles in a quadrilateral that are “next” to each other; they share a side 5. Opposite Sides: 6. Consecutive Sides:Mon, Jan 31
  8. 8. VOCABULARY 1. Quadrilateral: A four-sided figure 2. Parallelogram: A quadrilateral with two pairs of parallel sides 3. Opposite Angles: In a quadrilateral, the angles that do not share sides 4. Consecutive Angles: Angles in a quadrilateral that are “next” to each other; they share a side 5. Opposite Sides: Sides in a quadrilateral that do not touch each other 6. Consecutive Sides:Mon, Jan 31
  9. 9. VOCABULARY 1. Quadrilateral: A four-sided figure 2. Parallelogram: A quadrilateral with two pairs of parallel sides 3. Opposite Angles: In a quadrilateral, the angles that do not share sides 4. Consecutive Angles: Angles in a quadrilateral that are “next” to each other; they share a side 5. Opposite Sides: Sides in a quadrilateral that do not touch each other 6. Consecutive Sides: Sides in a quadrilateral that do touch each otherMon, Jan 31
  10. 10. QUADRILATERAL HIERARCHYMon, Jan 31
  11. 11. QUADRILATERAL HIERARCHY QuadrilateralMon, Jan 31
  12. 12. QUADRILATERAL HIERARCHY Quadrilateral 4 sidesMon, Jan 31
  13. 13. QUADRILATERAL HIERARCHY Quadrilateral 4 sides TrapezoidMon, Jan 31
  14. 14. QUADRILATERAL HIERARCHY Quadrilateral 4 sides Trapezoid 1 pair parallel sidesMon, Jan 31
  15. 15. QUADRILATERAL HIERARCHY Parallelogram Quadrilateral 4 sides Trapezoid 1 pair parallel sidesMon, Jan 31
  16. 16. QUADRILATERAL HIERARCHY Parallelogram Quadrilateral 2 pairs parallel 4 sides sides Trapezoid 1 pair parallel sidesMon, Jan 31
  17. 17. QUADRILATERAL HIERARCHY Parallelogram Quadrilateral 2 pairs parallel 4 sides sides Rectangle Trapezoid 1 pair parallel sidesMon, Jan 31
  18. 18. QUADRILATERAL HIERARCHY Parallelogram Quadrilateral 2 pairs parallel 4 sides sides Rectangle Opposite sides congruent, Trapezoid 90° angles 1 pair parallel sidesMon, Jan 31
  19. 19. QUADRILATERAL HIERARCHY Parallelogram Quadrilateral 2 pairs parallel 4 sides sides Rectangle Rhombus Opposite sides congruent, Trapezoid 90° angles 1 pair parallel sidesMon, Jan 31
  20. 20. QUADRILATERAL HIERARCHY Parallelogram Quadrilateral 2 pairs parallel 4 sides sides Rectangle Rhombus Opposite sides congruent, 4 equal Trapezoid 90° angles sides 1 pair parallel sidesMon, Jan 31
  21. 21. QUADRILATERAL HIERARCHY Parallelogram Quadrilateral 2 pairs parallel 4 sides sides Rectangle Rhombus Opposite sides congruent, 4 equal Trapezoid 90° angles sides 1 pair parallel sides SquareMon, Jan 31
  22. 22. QUADRILATERAL HIERARCHY Parallelogram Quadrilateral 2 pairs parallel 4 sides sides Rectangle Rhombus Opposite sides congruent, 4 equal Trapezoid 90° angles sides 1 pair parallel sides Square 4 equal sides 4 90° anglesMon, Jan 31
  23. 23. PROPERTIES OF PARALLELOGRAMSMon, Jan 31
  24. 24. PROPERTIES OF PARALLELOGRAMS 1. Opposites sides are congruentMon, Jan 31
  25. 25. PROPERTIES OF PARALLELOGRAMS 1. Opposites sides are congruent 2.Opposite angles are congruentMon, Jan 31
  26. 26. PROPERTIES OF PARALLELOGRAMS 1. Opposites sides are congruent 2.Opposite angles are congruent 3.Consecutive angles are supplementaryMon, Jan 31
  27. 27. PROPERTIES OF PARALLELOGRAMS 1. Opposites sides are congruent 2.Opposite angles are congruent 3.Consecutive angles are supplementary 4.The sum of the angles is 360°Mon, Jan 31
  28. 28. DIAGONALS OF PARALLELOGRAMSMon, Jan 31
  29. 29. DIAGONALS OF PARALLELOGRAMS 5.Diagonals bisect each otherMon, Jan 31
  30. 30. DIAGONALS OF PARALLELOGRAMS 5.Diagonals bisect each other 6.Diagonals of a rectangle are congruentMon, Jan 31
  31. 31. DIAGONALS OF PARALLELOGRAMS 5.Diagonals bisect each other 6.Diagonals of a rectangle are congruent 7. Diagonals of a rhombus are perpendicularMon, Jan 31
  32. 32. EXAMPLE 1 In parallelogram ABCD, diagonals AC and BD intersect at E. a. If AE = 5x - 3 and EC = 15 - x, find AC.Mon, Jan 31
  33. 33. EXAMPLE 1 In parallelogram ABCD, diagonals AC and BD intersect at E. a. If AE = 5x - 3 and EC = 15 - x, find AC.Mon, Jan 31
  34. 34. EXAMPLE 1 In parallelogram ABCD, diagonals AC and BD intersect at E. a. If AE = 5x - 3 and EC = 15 - x, find AC.Mon, Jan 31
  35. 35. EXAMPLE 1 In parallelogram ABCD, diagonals AC and BD intersect at E. a. If AE = 5x - 3 and EC = 15 - x, find AC.Mon, Jan 31
  36. 36. EXAMPLE 1 In parallelogram ABCD, diagonals AC and BD intersect at E. a. If AE = 5x - 3 and EC = 15 - x, find AC.Mon, Jan 31
  37. 37. EXAMPLE 1 In parallelogram ABCD, diagonals AC and BD intersect at E. a. If AE = 5x - 3 and EC = 15 - x, find AC. 6 6Mon, Jan 31
  38. 38. EXAMPLE 1 In parallelogram ABCD, diagonals AC and BD intersect at E. a. If AE = 5x - 3 and EC = 15 - x, find AC. 6 6 x=3Mon, Jan 31
  39. 39. EXAMPLE 1 In parallelogram ABCD, diagonals AC and BD intersect at E. a. If AE = 5x - 3 and EC = 15 - x, find AC. AE = EC = 6 6 x=3Mon, Jan 31
  40. 40. EXAMPLE 1 In parallelogram ABCD, diagonals AC and BD intersect at E. a. If AE = 5x - 3 and EC = 15 - x, find AC. AE = EC = 15 − 3 6 6 x=3Mon, Jan 31
  41. 41. EXAMPLE 1 In parallelogram ABCD, diagonals AC and BD intersect at E. a. If AE = 5x - 3 and EC = 15 - x, find AC. AE = EC = 15 − 3 = 12 6 6 x=3Mon, Jan 31
  42. 42. EXAMPLE 1 In parallelogram ABCD, diagonals AC and BD intersect at E. a. If AE = 5x - 3 and EC = 15 - x, find AC. AE = EC = 15 − 3 = 12 AC = AE + EC 6 6 x=3Mon, Jan 31
  43. 43. EXAMPLE 1 In parallelogram ABCD, diagonals AC and BD intersect at E. a. If AE = 5x - 3 and EC = 15 - x, find AC. AE = EC = 15 − 3 = 12 AC = AE + EC 6 AC = 12 + 12 6 x=3Mon, Jan 31
  44. 44. EXAMPLE 1 In parallelogram ABCD, diagonals AC and BD intersect at E. a. If AE = 5x - 3 and EC = 15 - x, find AC. AE = EC = 15 − 3 = 12 AC = AE + EC 6 AC = 12 + 12 6 x=3 AC = 24Mon, Jan 31
  45. 45. EXAMPLE 1 In parallelogram ABCD, diagonals AC and BD intersect at E. a. If AE = 5x - 3 and EC = 15 - x, find AC. AE = EC = 15 − 3 = 12 AC = AE + EC 6 AC = 12 + 12 6 x=3 AC = 24 unitsMon, Jan 31
  46. 46. EXAMPLE 1 In parallelogram ABCD, diagonals AC and BD intersect at E. b. If DE = 4y + 1 and EB = 5y - 1, find DB.Mon, Jan 31
  47. 47. EXAMPLE 1 In parallelogram ABCD, diagonals AC and BD intersect at E. b. If DE = 4y + 1 and EB = 5y - 1, find DB. 4y + 1 = 5y − 1Mon, Jan 31
  48. 48. EXAMPLE 1 In parallelogram ABCD, diagonals AC and BD intersect at E. b. If DE = 4y + 1 and EB = 5y - 1, find DB. 4y + 1 = 5y − 1 −4y +1 −4y +1Mon, Jan 31
  49. 49. EXAMPLE 1 In parallelogram ABCD, diagonals AC and BD intersect at E. b. If DE = 4y + 1 and EB = 5y - 1, find DB. 4y + 1 = 5y − 1 −4y +1 −4y +1 2=yMon, Jan 31
  50. 50. EXAMPLE 1 In parallelogram ABCD, diagonals AC and BD intersect at E. b. If DE = 4y + 1 and EB = 5y - 1, find DB. 4y + 1 = 5y − 1 DE = EB = −4y +1 −4y +1 2=yMon, Jan 31
  51. 51. EXAMPLE 1 In parallelogram ABCD, diagonals AC and BD intersect at E. b. If DE = 4y + 1 and EB = 5y - 1, find DB. 4y + 1 = 5y − 1 DE = EB = 4(2) + 1 −4y +1 −4y +1 2=yMon, Jan 31
  52. 52. EXAMPLE 1 In parallelogram ABCD, diagonals AC and BD intersect at E. b. If DE = 4y + 1 and EB = 5y - 1, find DB. 4y + 1 = 5y − 1 DE = EB = 4(2) + 1 = 9 −4y +1 −4y +1 2=yMon, Jan 31
  53. 53. EXAMPLE 1 In parallelogram ABCD, diagonals AC and BD intersect at E. b. If DE = 4y + 1 and EB = 5y - 1, find DB. 4y + 1 = 5y − 1 DE = EB = 4(2) + 1 = 9 −4y +1 −4y +1 DB = DE + EB 2=yMon, Jan 31
  54. 54. EXAMPLE 1 In parallelogram ABCD, diagonals AC and BD intersect at E. b. If DE = 4y + 1 and EB = 5y - 1, find DB. 4y + 1 = 5y − 1 DE = EB = 4(2) + 1 = 9 −4y +1 −4y +1 DB = DE + EB 2=y DB = 9 + 9Mon, Jan 31
  55. 55. EXAMPLE 1 In parallelogram ABCD, diagonals AC and BD intersect at E. b. If DE = 4y + 1 and EB = 5y - 1, find DB. 4y + 1 = 5y − 1 DE = EB = 4(2) + 1 = 9 −4y +1 −4y +1 DB = DE + EB 2=y DB = 9 + 9 DB = 18Mon, Jan 31
  56. 56. EXAMPLE 1 In parallelogram ABCD, diagonals AC and BD intersect at E. b. If DE = 4y + 1 and EB = 5y - 1, find DB. 4y + 1 = 5y − 1 DE = EB = 4(2) + 1 = 9 −4y +1 −4y +1 DB = DE + EB 2=y DB = 9 + 9 DB = 18 unitsMon, Jan 31
  57. 57. EXAMPLE 2 a. In quadrilateral ABCD, diagonals AC and BD intersect at E. What special quadrilateral must ABCD be so that AED is an isosceles triangle? Draw a picture first.Mon, Jan 31
  58. 58. EXAMPLE 2 a. In quadrilateral ABCD, diagonals AC and BD intersect at E. What special quadrilateral must ABCD be so that AED is an isosceles triangle? Draw a picture first. Discuss on edmodo, have an answer for class tomorrowMon, Jan 31
  59. 59. EXAMPLE 2 b. In rectangle ABCD, diagonals AC and BD intersect at E. Which pair of triangles is not congruent? Draw a picture first.Mon, Jan 31
  60. 60. EXAMPLE 2 b. In rectangle ABCD, diagonals AC and BD intersect at E. Which pair of triangles is not congruent? Draw a picture first. Discuss on edmodo, have an answer for class tomorrowMon, Jan 31
  61. 61. EXAMPLE 2 c. A woodworker makes parallel cuts XY and ZW in a board. The edges of the board, XZ and YW are also parallel. YW = 21.5 in. Find each measure, if possible. a. XZ b. m∠YXZ c. m∠XYW d. ZWMon, Jan 31
  62. 62. EXAMPLE 2 c. A woodworker makes parallel cuts XY and ZW in a board. The edges of the board, XZ and YW are also parallel. YW = 21.5 in. Find each measure, if possible. a. XZ b. m∠YXZ 21.5 in. c. m∠XYW d. ZWMon, Jan 31
  63. 63. EXAMPLE 2 c. A woodworker makes parallel cuts XY and ZW in a board. The edges of the board, XZ and YW are also parallel. YW = 21.5 in. Find each measure, if possible. a. XZ b. m∠YXZ 21.5 in. 135° c. m∠XYW d. ZWMon, Jan 31
  64. 64. EXAMPLE 2 c. A woodworker makes parallel cuts XY and ZW in a board. The edges of the board, XZ and YW are also parallel. YW = 21.5 in. Find each measure, if possible. a. XZ b. m∠YXZ 21.5 in. 135° c. m∠XYW d. ZW 45°Mon, Jan 31
  65. 65. EXAMPLE 2 c. A woodworker makes parallel cuts XY and ZW in a board. The edges of the board, XZ and YW are also parallel. YW = 21.5 in. Find each measure, if possible. a. XZ b. m∠YXZ 21.5 in. 135° c. m∠XYW d. ZW 45° Not enough infoMon, Jan 31
  66. 66. PROBLEM SETMon, Jan 31
  67. 67. PROBLEM SET p. 218 #1-43 odd “Make visible what, without you, might perhaps never have been seen.” - Robert BressonMon, Jan 31

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