1. Chapter 6
Quadrilaterals
Thompson

5. Special Quadrilaterals
Rhombus – four congruent sides
Square – four congruent sides and four congruent angles
Kite – two pairs of adjacent sides are congruent and no opposite sides are congruent
Trapezoid – Exactly one pair of parallel sides
Isosceles Trapezoid – the nonparallel sides are congruent.
Rectangle – four right angles
Parallelogram – both pairs of opposite sides are parallel

6. Classifying a Quadrilateral
Judging by appearance, classify ABCD in as many ways as possible.
Quadrilateral and Trapezoid

7. Relationships Among Special Quadrilaterals
Two pairs of parallel sides
No parallel sides
One pair of parallel sides
Parallelogram
Kite
Trapezoid
Rhombus
Rectangle
Isosceles Trapezoid
Square

8. Using the Properties of Special Quadrilaterals
In parallelogram RSTU, m Ð R = x – 10 and m Ð S = 3x Find x.

9. Closing . . .
ABCD is a square. Which classifications from this lesson apply to a square? Which do not apply?
A square is:
quadrilateral, parallelogram, rectangle, rhombus
A square is not:
trapezoid, kite

10. Classifying Quadrilaterals

11. Directions:
When the slide appears say the best name for the quadrilateral aloud.
Try to beat the computer by saying the answer before the computer in 4 seconds.

12. Best Name:

13. Best Name:
Isosceles
Trapezoid

14. Best Name:

15. Square Best Name: This quadrilateral is also: a rectangle a rhombus
a parallelogram

16. Best Name:

17. Best Name:
Quadrilateral

18. Best Name:

19. Best Name:
Rhombus
This quadrilateral is also:
a parallelogram

20. Best Name:

21. Best Name:
Quadrilateral

22. Best Name:

23. Best Name:
Rectangle
This quadrilateral is also:
a parallelogram

24. Best Name:

25. Best Name:
Isosceles
Trapezoid

26. Best Name:

27. Rhombus
Best Name:
This quadrilateral is also:
a parallelogram

28. Best Name:

29. Best Name:
Parallelogram

30. Best Name:

31. Best Name:
Trapezoid

32. Best Name:

33. Best Name:
Quadrilateral

34. Best Name:

35. Best Name:
Parallelogram

36. Best Name:

37. Best Name:
Trapezoid

38. Best Name:

39. Best Name:
Rectangle
This quadrilateral is also:
a parallelogram

40. Best Name:

41. Best Name:
Rhombus
This quadrilateral is also:
a parallelogram

42. Best Name:

43. Square Best Name: This quadrilateral is also: a rectangle a rhombus
a parallelogram

44. Best Name:

45. 2nd Stellation
Of Icosododecahedron

46. Game Over!

47. Classwork
Page 290
#’s 1-12, 19, 22, 23, , , 55

48. Properties of Parallelograms
Lesson 6-2

49. Key to remembering these!
We’re going to be learning a lot of similar looking theorems.
Draw a few pictures to see what happens.

50. Thm 6-1 Opposite sides of a parallelogram are congruent.
Other Properties of Parallelograms:
Opposite sides are parallel
Consecutive angles are supplementary

51. Using Consecutive Angles
Use parallelogram KMOQ to find m Ð O.
m Ð O = 145

52. Thm 6-2
Opposite angles of a parallelogram are congruent.

53. Thm 6-3
The diagonals of a parallelogram bisect each other.

54. Using Thms. 6-1 and 6-2
Find the value of x in parallelogram ABCD. Then find m Ð A.
m Ð A = 105

55. Example 1
Find the values of x and y.

56. Example 2
Find each indicated measure. NM KM
mJKL
mLKM

57. Thm 6-4
If three (or more) parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal.

58. Proving That a Quadrilateral is a Parallelogram
Lesson 6-3

59. Thm 6-5
If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.

60. Thm 6-6
If one pair of opposite sides of a quadrilateral is both congruent and parallel, then the quadrilateral is a parallelogram.

61. Finding Values for Parallelograms
Find values of x and y for which ABCD must be a parallelogram.
x = 18 and y = 89

62. Thm 6-7
If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

63. Thm 6-8
If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

65. Is the Quadrilateral a Parallelogram?
Determine whether the quadrilateral is a parallelogram. Explain.

66. Classwork
Page 297
#’s 18, 20, 40, 43, 46, 47
Page 307
#’s 7-15, 32-34