Quadrilaterals and Parallelograms

1. SECTION 5-6
Quadrilaterals and Parallelograms
Mon, Jan 31

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, navigation
Mon, Jan 31

3. VOCABULARY
1. Quadrilateral:
2. Parallelogram:
3. Opposite Angles:
4. Consecutive Angles:
5. Opposite Sides:
6. Consecutive Sides:
Mon, Jan 31

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. 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. 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. 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. 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. 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
other
Mon, Jan 31

10. QUADRILATERAL
HIERARCHY
Mon, Jan 31

11. QUADRILATERAL
HIERARCHY
Quadrilateral
Mon, Jan 31

12. QUADRILATERAL
HIERARCHY
Quadrilateral
4 sides
Mon, Jan 31

13. QUADRILATERAL
HIERARCHY
Quadrilateral
4 sides
Trapezoid
Mon, Jan 31

14. QUADRILATERAL
HIERARCHY
Quadrilateral
4 sides
Trapezoid
1 pair parallel
sides
Mon, Jan 31

15. QUADRILATERAL
HIERARCHY
Parallelogram
Quadrilateral
4 sides
Trapezoid
1 pair parallel
sides
Mon, Jan 31

16. QUADRILATERAL
HIERARCHY
Parallelogram
Quadrilateral
2 pairs parallel
4 sides sides
Trapezoid
1 pair parallel
sides
Mon, Jan 31

17. QUADRILATERAL
HIERARCHY
Parallelogram
Quadrilateral
2 pairs parallel
4 sides sides
Rectangle
Trapezoid
1 pair parallel
sides
Mon, Jan 31

18. QUADRILATERAL
HIERARCHY
Parallelogram
Quadrilateral
2 pairs parallel
4 sides sides
Rectangle
Opposite sides
congruent,
Trapezoid 90° angles
1 pair parallel
sides
Mon, Jan 31

19. QUADRILATERAL
HIERARCHY
Parallelogram
Quadrilateral
2 pairs parallel
4 sides sides
Rectangle Rhombus
Opposite sides
congruent,
Trapezoid 90° angles
1 pair parallel
sides
Mon, Jan 31

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
sides
Mon, Jan 31

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
Square
Mon, Jan 31

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° angles
Mon, Jan 31

23. PROPERTIES OF
PARALLELOGRAMS
Mon, Jan 31

24. PROPERTIES OF
PARALLELOGRAMS
1. Opposites sides are congruent
Mon, Jan 31

25. PROPERTIES OF
PARALLELOGRAMS
1. Opposites sides are congruent
2.Opposite angles are congruent
Mon, Jan 31

26. PROPERTIES OF
PARALLELOGRAMS
1. Opposites sides are congruent
2.Opposite angles are congruent
3.Consecutive angles are supplementary
Mon, Jan 31

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. DIAGONALS OF
PARALLELOGRAMS
Mon, Jan 31

29. DIAGONALS OF
PARALLELOGRAMS
5.Diagonals bisect each other
Mon, Jan 31

30. DIAGONALS OF
PARALLELOGRAMS
5.Diagonals bisect each other
6.Diagonals of a rectangle are congruent
Mon, Jan 31

31. DIAGONALS OF
PARALLELOGRAMS
5.Diagonals bisect each other
6.Diagonals of a rectangle are congruent
7. Diagonals of a rhombus are perpendicular
Mon, Jan 31

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. 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. 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. 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. 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. 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
Mon, Jan 31

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=3
Mon, Jan 31

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=3
Mon, Jan 31

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=3
Mon, Jan 31

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=3
Mon, Jan 31

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=3
Mon, Jan 31

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=3
Mon, Jan 31

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 = 24
Mon, Jan 31

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 units
Mon, Jan 31

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. 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
Mon, Jan 31

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 +1
Mon, Jan 31

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=y
Mon, Jan 31

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=y
Mon, Jan 31

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=y
Mon, Jan 31

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=y
Mon, Jan 31

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=y
Mon, Jan 31

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 + 9
Mon, Jan 31

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 = 18
Mon, Jan 31

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 units
Mon, Jan 31

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. 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 tomorrow
Mon, Jan 31

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. 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 tomorrow
Mon, Jan 31

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. ZW
Mon, Jan 31

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. ZW
Mon, Jan 31

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. ZW
Mon, Jan 31

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. 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 info
Mon, Jan 31

66. PROBLEM SET
Mon, Jan 31

67. PROBLEM SET
p. 218 #1-43 odd
“Make visible what, without you, might perhaps never have
been seen.” - Robert Bresson
Mon, Jan 31