1. The Quadrilateral Family Tree
Wednesday 12/3/08 –
Thursday 12/4/08

2. 1. _____________________
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2. _____________________
3. _____________________
4. _____________________
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3. _______________
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3. Quadrilateral 1. Four-sided polygon __________
1. _____________________
2. _____________________
3. _____________________
4. _____________________
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1. Four-sided polygon
1. _____________________
2. _____________________
3. _______________
__________
1. _____________________
_____________________
1. _____________________
2. _____________________
3. _____________________
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4. Parallelograms

5. Parallelogram
A quadrilateral with two pairs of parallel sides

6. Parallelogram QUADRILATERAL 1. Four-sided polygon Kite Trapezoid2. 3. 4.
Parallelogram
Square
Kite
Isosceles Trapezoid

7. Parallelogram

8. Parallelogram

9. Parallelogram 2 1

10. Parallelogram 2 1

11. Parallelogram 3 2 1 4

12. Parallelogram 3 2 1 4

13. Parallelogram 3 2 1 4

14. Parallelogram 3 2 1 4

15. Parallelogram
The two triangles formed by a diagonal are congruent by ASA. 3 2 1 4

16. Parallelogram
What does that mean about opposite sides of a parallelogram? 3 2 1 4

17. Parallelogram
What does that mean about opposite sides of a parallelogram? 3 2 1 4

18. Quadrilateral Kite Isosceles Trapezoid Rhombus Rectangle Square1.
TRAPEZOID
1. Four-sided polygon
Quadrilateral 2. 3. 4.
PARALLELOGRAM
Square
Rectangle
Rhombus
Kite
Isosceles Trapezoid

19. Parallelogram QUADRILATERAL 1. Four-sided polygon 1.2. 3. 4.
Parallelogram
Square 1.
1. Opposite sides are congruent 2. 3.

20. Parallelograms
What about opposite angles in a parallelogram?

21. Parallelogram QUADRILATERAL 1. Four-sided polygon 1.
2. Opposite angles are congruent 3. 4.
Parallelogram 2.
Square 1.
1. Opposite sides are congruent 2. 3.

22. Parallelograms Are these two triangles congruent? By which postulate?2 1

23. Parallelogram
Since the triangles are congruent, the diagonals of the parallelogram bisect each other.

24. Parallelogram QUADRILATERAL 1. Four-sided polygon 1.
2. Opposite angles are congruent
3. Diagonals bisect each other 4.
Parallelogram 2.
Square 3. 1.
1. Opposite sides are congruent 2. 3.

25. Parallelogram
What kind of angles are angles 5 & 6? 5 6

26. Parallelogram Consecutive angles in a parallelogram are supplementary.5 6

27. Parallelogram QUADRILATERAL 1. Four-sided polygon 1.
2. Opposite angles are congruent
3. Diagonals bisect each other
4. Consecutive angles are supp.
Parallelogram 2.
Square 3. 4. 1.
1. Opposite sides are congruent 2. 3.

28. Special Parallelograms
Rectangles, rhombuses, and squares

29. Rectangles

30. Rectangle
A quadrilateral with four right angles

31. Rectangle
Has all the properties of a parallelogram

32. Quadrilateral Parallelogram RECTANGLE 1. Four-sided polygon
2. Opposite angles are congruent
3. Diagonals bisect each other
4. Consecutive angles are supp.
Parallelogram 2.
Square
2. All properties above 3.
1. Four right angles
RECTANGLE 4.
1. Opposite sides are congruent

33. Rectangle
What should be true about the overlapping triangles formed by the diagonals?

34. Rectangle
What should be true about the overlapping triangles formed by the diagonals?

35. Rectangle
The triangles are congruent by SAS since opposite sides of a parallelogram are congruent

36. Rectangle
So the diagonals in a rectangle must be congruent by CPCTC

37. Quadrilateral Parallelogram RECTANGLE 1. Four-sided polygon
2. Opposite angles are congruent
3. Diagonals bisect each other
4. Consecutive angles are supp.
Parallelogram 2.
Square
2. All properties above
3. Diagonals are congruent
1. Four right angles
RECTANGLE 3. 4.
1. Opposite sides are congruent

38. Rhombuses

39. Rhombus
A quadrilateral with four congruent sides

40. Rhombus
Also has all the properties of a parallelogram

41. Quadrilateral Parallelogram RHOMBUS RECTANGLE 1. Four-sided polygon
2. Opposite angles are congruent
3. Diagonals bisect each other
4. Consecutive angles are supp.
Parallelogram 2.
Square
2. All properties above
3. Diagonals are congruent
1. Four right angles
RECTANGLE
1. Four congruent sides 3. 4.
RHOMBUS
1. Opposite sides are congruent

42. Rhombus
What kind of triangles are formed by a diagonal?

43. Rhombus
What kind of triangles are formed by a diagonal?

44. Rhombus
What kind of triangles are formed by a diagonal?

45. Rhombus
Each diagonal bisects a pair of opposite angles

46. Rhombus
Each diagonal bisects a pair of opposite angles

47. Quadrilateral Parallelogram RHOMBUS RECTANGLE 1. Four-sided polygon
2. Opposite angles are congruent
3. Diagonals bisect each other
4. Consecutive angles are supp.
Parallelogram 2.
Square
2. All properties above
3. Diagonals are congruent
1. Four right angles
RECTANGLE
1. Four congruent sides
3. Diagonals bisect opposite angles 4.
RHOMBUS 3.
1. Opposite sides are congruent

48. Rhombus

49. Rhombus
What should be true about angles 1 and 2? 2 1

50. Rhombus
What would the angle measures have to be? 2 1

51. Rhombus
What would the angle measures have to be?

52. Quadrilateral Parallelogram RHOMBUS RECTANGLE 1. Four-sided polygon
2. Opposite angles are congruent
3. Diagonals bisect each other
4. Consecutive angles are supp.
Parallelogram 2.
Square
2. All properties above
3. Diagonals are congruent
1. Four right angles
RECTANGLE
1. Four congruent sides
3. Diagonals bisect opposite angles
4. Diagonals are
RHOMBUS 3.
1. Opposite sides are congruent

53. Squares

54. Square
A quadrilateral with four right angles (like a rectangle) and four congruent sides (like a rhombus)

55. Square
So a square has all the properties of both a rectangle and a rhombus

56. Quadrilateral Parallelogram Rhombus Rectangle SQUARE1.
1. Four-sided polygon
Quadrilateral
2. Opposite angles are congruent
3. Diagonals bisect each other
4. Consecutive angles are supp.
Parallelogram
1. All properties of a rectangle
SQUARE
2. All properties above
3. Diagonals are congruent
1. Four right angles
Rectangle
1. Four congruent sides
3. Diagonals bisect opposite angles
4. Diagonals are
Rhombus 2. 3.
1. Opposite sides are congruent
2. All properties of a rhombus

57. Parallelograms
Rectangles
Rhombuses
Squares

58. Quadrilateral Kite Isosceles Trapezoid Rhombus Rectangle Square1.
TRAPEZOID
1. Four-sided polygon
Quadrilateral
1. Opposite sides are congruent
2. Opposite angles are congruent
3. Diagonals bisect each other
4. Consecutive angles are supplementary
PARALLELOGRAM
2. Properties of a rhombus
1. Properties of a rectangle
Square
2. Four right angles
3. Diagonals are congruent
1. All properties of a parallelogram
Rectangle
1. Properties of a parallelogram
2. All sides are congruent
3. Diagonals are perpendicular
4. Diagonals bisect opposite angles
Rhombus 2. 3.
Kite
Isosceles Trapezoid

59. Trapezoids

60. Trapezoid
A quadrilateral with exactly one pair of parallel sides

61. Parallelogram Square TRAPEZOID RHOMBUS RECTANGLE QUADRILATERAL
1. One pair of parallel sides
TRAPEZOID
1. Four-sided polygon
QUADRILATERAL
2. Opposite angles are congruent
3. Diagonals bisect each other
4. Consecutive angles are supp.
Parallelogram
1. All properties of a rectangle
Square
2. All properties above
3. Diagonals are congruent
1. Four right angles
RECTANGLE
1. Four congruent sides
3. Diagonals bisect opposite angles
4. Diagonals are
RHOMBUS 1. 2. 3.
1. Opposite sides are congruent
2. All properties of a rhombus

62. Trapezoid
If the legs are congruent, the trapezoid is an isosceles trapezoid

63. Quadrilateral Parallelogram Rhombus TRAPEZOID ISOSCELES TRAPEZOID
1. One pair of parallel sides
TRAPEZOID
1. Four-sided polygon
Quadrilateral
2. Opposite angles are congruent
3. Diagonals bisect each other
4. Consecutive angles are supp.
Parallelogram
1. All properties of a rectangle
SQUARE
2. All properties above
3. Diagonals are congruent
1. Four right angles
RECTANGLE
1. Four congruent sides
3. Diagonals bisect opposite angles
4. Diagonals are
Rhombus
1. Legs are congruent 2. 3.
ISOSCELES TRAPEZOID
1. Opposite sides are congruent 1.
2. All properties of a rhombus

64. Isosceles Trapezoid

65. Isosceles Trapezoid
In an isosceles trapezoid, the base angles are congruent

66. Quadrilateral Parallelogram Rhombus TRAPEZOID ISOSCELES TRAPEZOID
1. One pair of parallel sides
TRAPEZOID
1. Four-sided polygon
Quadrilateral
2. Opposite angles are congruent
3. Diagonals bisect each other
4. Consecutive angles are supp.
Parallelogram
1. All properties of a rectangle
SQUARE
2. All properties above
3. Diagonals are congruent
1. Four right angles
RECTANGLE
1. Four congruent sides
3. Diagonals bisect opposite angles
4. Diagonals are
Rhombus
1. Legs are congruent
2. Base <s are congruent 3.
ISOSCELES TRAPEZOID
1. Opposite sides are congruent 2. 1.
2. All properties of a rhombus

67. Isosceles Trapezoid
What should be true about the diagonals of an isosceles trapezoid?

68. Isosceles Trapezoid
What should be true about the diagonals of an isosceles trapezoid?

69. Quadrilateral Parallelogram Rhombus Square TRAPEZOID
1. One pair of parallel sides
TRAPEZOID
1. Four-sided polygon
Quadrilateral
2. Opposite angles are congruent
3. Diagonals bisect each other
4. Consecutive angles are supp.
Parallelogram
1. All properties of a rectangle
Square
2. All properties above
3. Diagonals are congruent
1. Four right angles
RECTANGLE
1. Four congruent sides
3. Diagonals bisect opposite angles
4. Diagonals are
Rhombus
1. Legs are congruent
2. Base <s are congruent
ISOSCELES TRAPEZOID
1. Opposite sides are congruent 2. 3. 1.
2. All properties of a rhombus

70. Trapezoid Midsegment
The segment formed by the midpoints of the legs

71. Trapezoid Midsegment
Its length is the average of the two bases.

72. Trapezoid Midsegment
Its length is the average of the two bases.

73. Kites

74. Kite
A quadrilateral with exactly two pairs of congruent consecutive sides

75. 1. 2 pairs of congruent consecutive sides
1. One pair of parallel sides
Trapezoid
1. Four-sided polygon
QUADRILATERAL
2. Opposite angles are congruent
3. Diagonals bisect each other
4. Consecutive angles are supp.
Parallelogram
1. All properties of a rectangle
Square
2. All properties above
3. Diagonals are congruent
1. Four right angles
RECTANGLE
1. Four congruent sides
3. Diagonals bisect opposite angles
4. Diagonals are
RHOMBUS
Kite
1. Legs are congruent
2. Base <s are congruent
Isosceles Trapezoid
1. Opposite sides are congruent 2. 3.
1. 2 pairs of congruent consecutive sides
2. All properties of a rhombus

76. Kite
Diagonals are perpendicular

77. 1. 2 pairs of congruent consecutive sides
1. One pair of parallel sides
Trapezoid
1. Four-sided polygon
QUADRILATERAL
2. Opposite angles are congruent
3. Diagonals bisect each other
4. Consecutive angles are supp.
Parallelogram
1. All properties of a rectangle
Square
2. All properties above
3. Diagonals are congruent
1. Four right angles
RECTANGLE
1. Four congruent sides
3. Diagonals bisect opposite angles
4. Diagonals are
RHOMBUS
Kite
1. Legs are congruent
2. Base <s are congruent
Isosceles Trapezoid
1. Opposite sides are congruent
2. Diagonals are _ 3.
1. 2 pairs of congruent consecutive sides
2. All properties of a rhombus

78. Kite
Exactly one pair of opposite angles are congruent

79. 3. One pair of opposite <s congruent
1. One pair of parallel sides
Trapezoid
1. Four-sided polygon
QUADRILATERAL
2. Opposite angles are congruent
3. Diagonals bisect each other
4. Consecutive angles are supp.
Parallelogram
1. All properties of a rectangle
Square
2. All properties above
3. Diagonals are congruent
1. Four right angles
RECTANGLE
1. Four congruent sides
3. Diagonals bisect opposite angles
4. Diagonals are
RHOMBUS
Kite
1. Legs are congruent
2. Base <s are congruent
Isosceles Trapezoid
1. Opposite sides are congruent
2. Diagonals are _
3. One pair of opposite <s congruent
1. 2 pairs of congruent consecutive sides
2. All properties of a rhombus

80. Quadrilateral Kite Isosceles Trapezoid Rhombus Rectangle Square
1. Exactly one pair of parallel sides
TRAPEZOID
1. Four-sided polygon
Quadrilateral
1. Opposite sides are congruent
2. Opposite angles are congruent
3. Diagonals bisect each other
4. Consecutive angles are supplementary
PARALLELOGRAM
2. Properties of a rhombus
1. Properties of a rectangle
Square
2. Four right angles
3. Diagonals are congruent
1. All properties of a parallelogram
Rectangle
1. Properties of a parallelogram
2. All sides are congruent
3. Diagonals are perpendicular
4. Diagonals bisect opposite angles
Rhombus
1. Exactly two pairs of congruent sides
2. Exactly one pair of congruent opposite angles
3. Diagonals are perpendicular
Kite
1. Legs are congruent
2. Diagonals are congruent
3. Two pairs of congruent base angles
Isosceles Trapezoid