1. 6.6Trapezoids and Kites Last set of quadrilateral properties

2. Terminology:

3. Trapezoi d Kite

4. Terminology: Trapezoi d Quadrilateral with exactly one pair of parallel sides. Kite

5. Terminology: Trapezoi d Quadrilateral with exactly one pair of parallel sides. KiteQuadrilateral with two pairs of consecutive congruent sides, none of which are parallel.

6. Start with the trapezoid

8. O Parallel sides are called bases

9. Start with the trapezoid O Non parallel sides are called legs.

10. Start with the trapezoid O Since one pair is parallel

11. Start with the trapezoid O Since one pair is parallel Angles on the same leg are supplementary.

12. Now for the special

13. O Isosceles trapezoid is a trapezoid whose legs are congruent.

14. And now for the proof, drawing in perpendiculars A B C D E F

15. A B C D E F

16. A B C D E F

17. A B C D E F

18. As a result,  ACE   BDF by? A B C D E F

19.  C   D by… A B C D E F

20. As a result,  A   B by… A B C D E F

21. Theorem 6-19: If a quadrilateral is an isosceles trapezoid, then each pair of base  ’s is . A B C D E F

22. Make sure you can…

23. O Given one angle of an isosceles trapezoid, find the remaining 3 angles.

24. Application: page 390 Problem 2

25. Focusing on 1 section

26. AC  BD because? A B E C D

27.  C   D by? A B E C D

28. If we want to prove  ’s ACD and BCD are congruent, what do they share? A B E C D

29.  ACD  BCD by A B E C D

30. AD  BC by A B E C D

31. Theorem 6-20: If a quadrilateral is an isosceles trapezoid, then its diagonals are  A B E C D

32. The return of midsegments

33. The return of midsegments A midsegment of a trapezoid connects the midpoints of the legs (non parallel sides) and is the mean value of the 2 bases (parallel sides)

34. The return of midsegments A midsegment of a trapezoid connects the midpoints of the legs (non parallel sides) and is the mean value of the 2 bases (parallel sides)

35. In addition… A midsegment of a trapezoid connects the midpoints of the legs (non parallel sides) and is the mean value of the 2 bases (parallel sides)

36. In addition… Much like triangles, the midsegment is parallel to the sides it does not touch.

37. So find its length?

38. O Add the bases and divide by 2.

39. Working backwards

40. O Formula:

41. Working backwards

42. Plug in the length of the midsegment.

43. Plug in the length of a base.

44. Solve for the remaining base

45. O Or

46. Solve for the remaining base O Or O Arithmetically, multiply the length of the midsegment by 2 and subtract the length of the given base.

47. Here’s a problem I enjoy. O Given an isosceles trapezoid whose midsegment measures 50 cm and whose legs measures 24 mm. Find its perimeter.

48. Now to kites:

49. If we drew in a line of symmetry, where would it be?

50. And now are there   ’s?

51.  KEY   TEY

52. What new is congruent by CPCTC?

53. These are called the non-vertex angles, because they connect the non congruent sides

54. What else is congruent by CPCTC

55. What else is congruent by CPCTC?

56. The original angles, E and Y, are the vertex angles, and we can conclude they are bisected by the diagonal.

57. The vertex angles of a kite are the common endpoints of the congruent sides.

58. Summarizing

59. O Vertex angles connect the congruent sides and are bisected by the diagonals.

60. Summarizing O Vertex angles connect the congruent sides and are bisected by the diagonals. O Non vertex angles connect the non-congruent sides and are congruent.

61. One last property that becomes Theorem 6-22

62. If we draw in both diagonals…

63. If a quadrilateral is a kite, then its diagonals are perpendicular.

64. Problem solving examples

65. The family tree of quadrilaterals

68. Which group breaks down more?

71. And if we combine the last 2?

74. Those are all the definitions

75. O You need to remember all the properties, especially the ones that work for parallelograms, since they also work for a rhombus, rectangle, and square.

76. In addition… O You need to remember all the properties, especially the ones that work for parallelograms, since they also work for a rhombus, rectangle, and square.

77. In addition… O You need to determine the truth value (true/false) of a universal statement

78. In addition… O You need to determine the truth value (true/false) of a universal statement O All rectangles are parallelograms.

79. In addition… O You need to determine the truth value (true/false) of a universal statement O All rhombi are squares.