6.6 Trapezoids and Kites - PowerPoint PPT Presentation

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6.6 Trapezoids and Kites

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  1. 6.6 Trapezoids and Kites Last set of quadrilateral properties

  2. Terminology:

  3. Terminology:

  4. Terminology:

  5. Terminology:

  6. Start with the trapezoid

  7. Start with the trapezoid

  8. Start with the trapezoid • Parallel sides are called bases

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

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

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

  12. Now for the special

  13. Now for the special • 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. Why is ? A B C D E F

  16. Remember, A B C D E F

  17. Why is ? 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. Make sure you can… • 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. So find its length? • Add the bases and divide by 2.

  39. Working backwards

  40. Working backwards • Formula:

  41. Working backwards • Formula: • Midsegment =

  42. Plug in the length of the midsegment. • Formula: • Midsegment =

  43. Plug in the length of a base. • Formula: • Midsegment =

  44. Solve for the remaining base • Formula: • Midsegment =

  45. Solve for the remaining base • Or

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

  47. Here’s a problem I enjoy. • 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?