1. Section 6-6 Trapezoids and Kites Tuesday, April 29, 14

2. Essential Questions How do you apply properties of trapezoids? How do you apply properties of kites? Tuesday, April 29, 14

3. Vocabulary 1.Trapezoid: 2. Bases: 3. Legs of a Trapezoid: 4. Base Angles: 5. Isosceles Trapezoid: Tuesday, April 29, 14

4. Vocabulary 1.Trapezoid: A quadrilateral with only one pair of parallel sides 2. Bases: 3. Legs of a Trapezoid: 4. Base Angles: 5. Isosceles Trapezoid: Tuesday, April 29, 14

5. Vocabulary 1.Trapezoid: A quadrilateral with only one pair of parallel sides 2. Bases: The parallel sides of a trapezoid 3. Legs of a Trapezoid: 4. Base Angles: 5. Isosceles Trapezoid: Tuesday, April 29, 14

6. Vocabulary 1.Trapezoid: A quadrilateral with only one pair of parallel sides 2. Bases: The parallel sides of a trapezoid 3. Legs of a Trapezoid: The sides that are not parallel in a trapezoid 4. Base Angles: 5. Isosceles Trapezoid: Tuesday, April 29, 14

7. Vocabulary 1.Trapezoid: A quadrilateral with only one pair of parallel sides 2. Bases: The parallel sides of a trapezoid 3. Legs of a Trapezoid: The sides that are not parallel in a trapezoid 4. Base Angles: The angles formed between a base and one of the legs 5. Isosceles Trapezoid: Tuesday, April 29, 14

8. Vocabulary 1.Trapezoid: A quadrilateral with only one pair of parallel sides 2. Bases: The parallel sides of a trapezoid 3. Legs of a Trapezoid: The sides that are not parallel in a trapezoid 4. Base Angles: The angles formed between a base and one of the legs 5. Isosceles Trapezoid: A trapezoid that has congruent legs Tuesday, April 29, 14

9. Vocabulary 6. Midsegment of a Trapezoid: 7. Kite: Tuesday, April 29, 14

10. Vocabulary 6. Midsegment of a Trapezoid: The segment that connects the midpoints of the legs of a trapezoid 7. Kite: Tuesday, April 29, 14

11. Vocabulary 6. Midsegment of a Trapezoid: The segment that connects the midpoints of the legs of a trapezoid 7. Kite: A quadrilateral with exactly two pairs of consecutive congruent sides; Opposite sides are not parallel or congruent Tuesday, April 29, 14

12. Theorems Isosceles Trapezoid 6.21: 6.22: 6.23: Tuesday, April 29, 14

13. Theorems Isosceles Trapezoid 6.21: If a trapezoid is isosceles, then each pair of base angles is congruent 6.22: 6.23: Tuesday, April 29, 14

14. Theorems Isosceles Trapezoid 6.21: If a trapezoid is isosceles, then each pair of base angles is congruent 6.22: If a trapezoid has one pair of congruent base angles, then it is isosceles 6.23: Tuesday, April 29, 14

15. Theorems Isosceles Trapezoid 6.21: If a trapezoid is isosceles, then each pair of base angles is congruent 6.22: If a trapezoid has one pair of congruent base angles, then it is isosceles 6.23: A trapezoid is isosceles IFF its diagonals are congruent Tuesday, April 29, 14

16. Theorems 6.24 - Trapezoid Midsegment Theorem: Kites 6.25: 6.26: Tuesday, April 29, 14

17. Theorems 6.24 - Trapezoid Midsegment Theorem: The midsegment of a trapezoid is parallel to each base and its measure is half of the sum of the lengths of the two bases Kites 6.25: 6.26: Tuesday, April 29, 14

18. Theorems 6.24 - Trapezoid Midsegment Theorem: The midsegment of a trapezoid is parallel to each base and its measure is half of the sum of the lengths of the two bases Kites 6.25: If a quadrilateral is a kite, then its diagonals are perpendicular 6.26: Tuesday, April 29, 14

19. Theorems 6.24 - Trapezoid Midsegment Theorem: The midsegment of a trapezoid is parallel to each base and its measure is half of the sum of the lengths of the two bases Kites 6.25: If a quadrilateral is a kite, then its diagonals are perpendicular 6.26: If a quadrilateral is a kite, then exactly one pair of opposite angles is congruent Tuesday, April 29, 14

20. Example 1 Each side of a basket is an isosceles trapezoid. If mJML = 130, KN = 6.7 ft, and LN = 3.6 ft, nd each measure. a. mMJK Tuesday, April 29, 14

21. Example 1 Each side of a basket is an isosceles trapezoid. If mJML = 130, KN = 6.7 ft, and LN = 3.6 ft, nd each measure. a. mMJK mJML = mKLM Tuesday, April 29, 14

22. Example 1 Each side of a basket is an isosceles trapezoid. If mJML = 130, KN = 6.7 ft, and LN = 3.6 ft, nd each measure. a. mMJK mJML = mKLM 360 2(130) Tuesday, April 29, 14

23. Example 1 Each side of a basket is an isosceles trapezoid. If mJML = 130, KN = 6.7 ft, and LN = 3.6 ft, nd each measure. a. mMJK mJML = mKLM 360 2(130) = 100 Tuesday, April 29, 14

24. Example 1 Each side of a basket is an isosceles trapezoid. If mJML = 130, KN = 6.7 ft, and LN = 3.6 ft, nd each measure. a. mMJK mJML = mKLM 360 2(130) = 100 100/2 Tuesday, April 29, 14

25. Example 1 Each side of a basket is an isosceles trapezoid. If mJML = 130, KN = 6.7 ft, and LN = 3.6 ft, nd each measure. a. mMJK mJML = mKLM 360 2(130) = 100 100/2 = 50 Tuesday, April 29, 14

26. Example 1 Each side of a basket is an isosceles trapezoid. If mJML = 130, KN = 6.7 ft, and LN = 3.6 ft, nd each measure. a. mMJK mJML = mKLM 360 2(130) = 100 100/2 = 50 mMJK = 50 Tuesday, April 29, 14

27. Example 1 Each side of a basket is an isosceles trapezoid. If mJML = 130, KN = 6.7 ft, and LN = 3.6 ft, nd each measure. b. JL Tuesday, April 29, 14

28. Example 1 Each side of a basket is an isosceles trapezoid. If mJML = 130, KN = 6.7 ft, and LN = 3.6 ft, nd each measure. b. JL JN = KN Tuesday, April 29, 14

29. Example 1 Each side of a basket is an isosceles trapezoid. If mJML = 130, KN = 6.7 ft, and LN = 3.6 ft, nd each measure. b. JL JN = KN JL = JN + LN Tuesday, April 29, 14

30. Example 1 Each side of a basket is an isosceles trapezoid. If mJML = 130, KN = 6.7 ft, and LN = 3.6 ft, nd each measure. b. JL JN = KN JL = JN + LN JL = 6.7 + 3.6 Tuesday, April 29, 14

31. Example 1 Each side of a basket is an isosceles trapezoid. If mJML = 130, KN = 6.7 ft, and LN = 3.6 ft, nd each measure. b. JL JN = KN JL = JN + LN JL = 6.7 + 3.6 JL = 10.3 ft Tuesday, April 29, 14

32. Example 2 Quadrilateral ABCD has vertices A(5, 1), B(3, 1), C(2, 3), and D(2, 4). Show that ABCD is a trapezoid and determine whether it is an isosceles trapezoid. Tuesday, April 29, 14

33. Example 2 Quadrilateral ABCD has vertices A(5, 1), B(3, 1), C(2, 3), and D(2, 4). Show that ABCD is a trapezoid and determine whether it is an isosceles trapezoid. x y Tuesday, April 29, 14

34. Example 2 Quadrilateral ABCD has vertices A(5, 1), B(3, 1), C(2, 3), and D(2, 4). Show that ABCD is a trapezoid and determine whether it is an isosceles trapezoid. x y A Tuesday, April 29, 14

35. Example 2 Quadrilateral ABCD has vertices A(5, 1), B(3, 1), C(2, 3), and D(2, 4). Show that ABCD is a trapezoid and determine whether it is an isosceles trapezoid. x y A B Tuesday, April 29, 14

36. Example 2 Quadrilateral ABCD has vertices A(5, 1), B(3, 1), C(2, 3), and D(2, 4). Show that ABCD is a trapezoid and determine whether it is an isosceles trapezoid. x y A B C Tuesday, April 29, 14

37. Example 2 Quadrilateral ABCD has vertices A(5, 1), B(3, 1), C(2, 3), and D(2, 4). Show that ABCD is a trapezoid and determine whether it is an isosceles trapezoid. x y A B C D Tuesday, April 29, 14

38. Example 2 Quadrilateral ABCD has vertices A(5, 1), B(3, 1), C(2, 3), and D(2, 4). Show that ABCD is a trapezoid and determine whether it is an isosceles trapezoid. x y A B C D Tuesday, April 29, 14

39. Example 2 Quadrilateral ABCD has vertices A(5, 1), B(3, 1), C(2, 3), and D(2, 4). Show that ABCD is a trapezoid and determine whether it is an isosceles trapezoid. x y A B C D We need AB to be parallel with CD Tuesday, April 29, 14

40. Example 2 Quadrilateral ABCD has vertices A(5, 1), B(3, 1), C(2, 3), and D(2, 4). Show that ABCD is a trapezoid and determine whether it is an isosceles trapezoid. x y A B C D We need AB to be parallel with CD CB ADAlso, Tuesday, April 29, 14

41. Example 2 A(5, 1), B(3, 1), C(2, 3), and D(2, 4) Tuesday, April 29, 14

42. Example 2 A(5, 1), B(3, 1), C(2, 3), and D(2, 4) m(AB) = 11 3 5 Tuesday, April 29, 14

43. Example 2 A(5, 1), B(3, 1), C(2, 3), and D(2, 4) m(AB) = 11 3 5 = 2 8 Tuesday, April 29, 14

44. Example 2 A(5, 1), B(3, 1), C(2, 3), and D(2, 4) m(AB) = 11 3 5 = 2 8 = 1 4 Tuesday, April 29, 14

45. Example 2 A(5, 1), B(3, 1), C(2, 3), and D(2, 4) m(AB) = 11 3 5 = 2 8 = 1 4 m(CD) = 4 3 2 (2) Tuesday, April 29, 14

46. Example 2 A(5, 1), B(3, 1), C(2, 3), and D(2, 4) m(AB) = 11 3 5 = 2 8 = 1 4 m(CD) = 4 3 2 (2) = 1 4 Tuesday, April 29, 14

47. Example 2 A(5, 1), B(3, 1), C(2, 3), and D(2, 4) m(AB) = 11 3 5 = 2 8 = 1 4 m(CD) = 4 3 2 (2) = 1 4 AD = (5 2)2 + (1 4)2 Tuesday, April 29, 14

48. Example 2 A(5, 1), B(3, 1), C(2, 3), and D(2, 4) m(AB) = 11 3 5 = 2 8 = 1 4 m(CD) = 4 3 2 (2) = 1 4 AD = (5 2)2 + (1 4)2 = (3)2 + (3)2 Tuesday, April 29, 14

49. Example 2 A(5, 1), B(3, 1), C(2, 3), and D(2, 4) m(AB) = 11 3 5 = 2 8 = 1 4 m(CD) = 4 3 2 (2) = 1 4 AD = (5 2)2 + (1 4)2 = (3)2 + (3)2 = 9 + 9 Tuesday, April 29, 14

50. Example 2 A(5, 1), B(3, 1), C(2, 3), and D(2, 4) m(AB) = 11 3 5 = 2 8 = 1 4 m(CD) = 4 3 2 (2) = 1 4 AD = (5 2)2 + (1 4)2 = (3)2 + (3)2 = 9 + 9 = 18 Tuesday, April 29, 14

51. Example 2 A(5, 1), B(3, 1), C(2, 3), and D(2, 4) m(AB) = 11 3 5 = 2 8 = 1 4 m(CD) = 4 3 2 (2) = 1 4 AD = (5 2)2 + (1 4)2 = (3)2 + (3)2 = 9 + 9 = 18 BC = (3+ 2)2 + (1 3)2 Tuesday, April 29, 14

52. Example 2 A(5, 1), B(3, 1), C(2, 3), and D(2, 4) m(AB) = 11 3 5 = 2 8 = 1 4 m(CD) = 4 3 2 (2) = 1 4 AD = (5 2)2 + (1 4)2 = (3)2 + (3)2 = 9 + 9 = 18 BC = (3+ 2)2 + (1 3)2 = (1)2 + (4)2 Tuesday, April 29, 14

53. Example 2 A(5, 1), B(3, 1), C(2, 3), and D(2, 4) m(AB) = 11 3 5 = 2 8 = 1 4 m(CD) = 4 3 2 (2) = 1 4 AD = (5 2)2 + (1 4)2 = (3)2 + (3)2 = 9 + 9 = 18 BC = (3+ 2)2 + (1 3)2 = (1)2 + (4)2 = 1+16 Tuesday, April 29, 14

54. Example 2 A(5, 1), B(3, 1), C(2, 3), and D(2, 4) m(AB) = 11 3 5 = 2 8 = 1 4 m(CD) = 4 3 2 (2) = 1 4 AD = (5 2)2 + (1 4)2 = (3)2 + (3)2 = 9 + 9 = 18 BC = (3+ 2)2 + (1 3)2 = (1)2 + (4)2 = 1+16 = 17 Tuesday, April 29, 14

55. Example 2 A(5, 1), B(3, 1), C(2, 3), and D(2, 4) m(AB) = 11 3 5 = 2 8 = 1 4 m(CD) = 4 3 2 (2) = 1 4 AD = (5 2)2 + (1 4)2 = (3)2 + (3)2 = 9 + 9 = 18 BC = (3+ 2)2 + (1 3)2 = (1)2 + (4)2 = 1+16 = 17 CB AD Tuesday, April 29, 14

56. Example 2 A(5, 1), B(3, 1), C(2, 3), and D(2, 4) m(AB) = 11 3 5 = 2 8 = 1 4 m(CD) = 4 3 2 (2) = 1 4 AD = (5 2)2 + (1 4)2 = (3)2 + (3)2 = 9 + 9 = 18 BC = (3+ 2)2 + (1 3)2 = (1)2 + (4)2 = 1+16 = 17 It is a trapezoid, but not isoscelesCB AD Tuesday, April 29, 14

57. Example 3 In the gure, MN is the midsegment of trapezoid FGJK. What is the value of x? Tuesday, April 29, 14

58. Example 3 In the gure, MN is the midsegment of trapezoid FGJK. What is the value of x? MN = KF + JG 2 Tuesday, April 29, 14

59. Example 3 In the gure, MN is the midsegment of trapezoid FGJK. What is the value of x? MN = KF + JG 2 30 = 20 + JG 2 Tuesday, April 29, 14

60. Example 3 In the gure, MN is the midsegment of trapezoid FGJK. What is the value of x? MN = KF + JG 2 30 = 20 + JG 2 60 = 20 + JG Tuesday, April 29, 14

61. Example 3 In the gure, MN is the midsegment of trapezoid FGJK. What is the value of x? MN = KF + JG 2 30 = 20 + JG 2 60 = 20 + JG 40 = JG Tuesday, April 29, 14

62. Example 4 If WXYZ is a kite, nd mXYZ. Tuesday, April 29, 14

63. Example 4 If WXYZ is a kite, nd mXYZ. mWXY = mWZY Tuesday, April 29, 14

64. Example 4 If WXYZ is a kite, nd mXYZ. mWXY = mWZY mXYZ = 360 121 73121 Tuesday, April 29, 14

65. Example 4 If WXYZ is a kite, nd mXYZ. mWXY = mWZY mXYZ = 360 121 73121 = 45 Tuesday, April 29, 14

66. Example 5 If MNPQ is a kite, nd NP. Tuesday, April 29, 14

67. Example 5 If MNPQ is a kite, nd NP. a2 + b2 = c2 Tuesday, April 29, 14

68. Example 5 If MNPQ is a kite, nd NP. a2 + b2 = c2 62 + 82 = c2 Tuesday, April 29, 14

69. Example 5 If MNPQ is a kite, nd NP. a2 + b2 = c2 62 + 82 = c2 36 + 64 = c2 Tuesday, April 29, 14

70. Example 5 If MNPQ is a kite, nd NP. a2 + b2 = c2 62 + 82 = c2 36 + 64 = c2 100 = c2 Tuesday, April 29, 14

71. Example 5 If MNPQ is a kite, nd NP. a2 + b2 = c2 62 + 82 = c2 36 + 64 = c2 100 = c2 100 = c2 Tuesday, April 29, 14

72. Example 5 If MNPQ is a kite, nd NP. a2 + b2 = c2 62 + 82 = c2 36 + 64 = c2 100 = c2 100 = c2 c =10 Tuesday, April 29, 14

73. Problem Set Tuesday, April 29, 14

74. Problem Set p. 440 #1-27 odd, 35-43 odd, 49, 65, 75, 77 Do what you love, love what you do, leave the world a better place and don't pick your nose. - Jeff Mallett Tuesday, April 29, 14