Geometry Section 6-6 1112
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Trapezoid
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- 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