Quadrilaterals and Parallelograms

1. SECTION 5-6
Quadrilaterals and Parallelograms

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

3. VOCABULARY
1. Quadrilateral:
2. Parallelogram:
3. Opposite Angles:
4. Consecutive Angles:
5. Opposite Sides:
6. Consecutive Sides:

4. VOCABULARY
1. Quadrilateral: A four-sided figure
2. Parallelogram:
3. Opposite Angles:
4. Consecutive Angles:
5. Opposite Sides:
6. Consecutive Sides:

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:

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:

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:

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:

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

10. QUADRILATERAL
HIERARCHY

11. QUADRILATERAL
HIERARCHY
Quadrilateral

12. QUADRILATERAL
HIERARCHY
Quadrilateral
4 sides

13. QUADRILATERAL
HIERARCHY
Quadrilateral
4 sides
Trapezoid

14. QUADRILATERAL
HIERARCHY
Quadrilateral
4 sides
Trapezoid
1 pair parallel
sides

15. QUADRILATERAL
HIERARCHY
Parallelogram
Quadrilateral
4 sides
Trapezoid
1 pair parallel
sides

16. QUADRILATERAL
HIERARCHY
Parallelogram
Quadrilateral
2 pairs parallel
4 sides sides
Trapezoid
1 pair parallel
sides

17. QUADRILATERAL
HIERARCHY
Parallelogram
Quadrilateral
2 pairs parallel
4 sides sides
Rectangle
Trapezoid
1 pair parallel
sides

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

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

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

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

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

23. PROPERTIES OF
PARALLELOGRAMS

24. PROPERTIES OF
PARALLELOGRAMS
1. Opposites sides are congruent

25. PROPERTIES OF
PARALLELOGRAMS
1. Opposites sides are congruent
2.Opposite angles are congruent

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

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°

28. DIAGONALS OF
PARALLELOGRAMS

29. DIAGONALS OF
PARALLELOGRAMS
5.Diagonals bisect each other

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

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

32. EXAMPLE 1
In parallelogram ABCD, diagonals AC and BD intersect at E.
a. If AE = 5x - 3 and EC = 15 - x, find AC.

33. EXAMPLE 1
In parallelogram ABCD, diagonals AC and BD intersect at E.
a. If AE = 5x - 3 and EC = 15 - x, find AC.

34. EXAMPLE 1
In parallelogram ABCD, diagonals AC and BD intersect at E.
a. If AE = 5x - 3 and EC = 15 - x, find AC.

35. EXAMPLE 1
In parallelogram ABCD, diagonals AC and BD intersect at E.
a. If AE = 5x - 3 and EC = 15 - x, find AC.

36. EXAMPLE 1
In parallelogram ABCD, diagonals AC and BD intersect at E.
a. If AE = 5x - 3 and EC = 15 - x, find AC.

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

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

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

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

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

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

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

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

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

46. EXAMPLE 1
In parallelogram ABCD, diagonals AC and BD intersect at E.
b. If DE = 4y + 1 and EB = 5y - 1, find DB.

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

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

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

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

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

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

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

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

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

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

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.

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.
Class poll and discussion

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.

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.
Class poll and discussion

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

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

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

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°

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

66. HOMEWORK

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