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OpenSessame Group Title

Find the midpoint of each side of the trapezoid. Connect the midpoints. What is the most precise classification of the quadrilateral formed by connecting the midpoints of the sides of the trapezoid?

  • 11 months ago
  • 11 months ago

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  1. OpenSessame Group Title
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    |dw:1377490333537:dw|

    • 11 months ago
  2. mathstudent55 Group Title
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    I just made it a bit bigger. |dw:1377490546842:dw|

    • 11 months ago
  3. mathstudent55 Group Title
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    |dw:1377490654352:dw|

    • 11 months ago
  4. OpenSessame Group Title
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    So I know the answer is, The rhombus is a square but i need help finding midpoints.

    • 11 months ago
  5. mathstudent55 Group Title
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    We can label all midpoints.

    • 11 months ago
  6. OpenSessame Group Title
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    Im guessing|dw:1377490680684:dw|

    • 11 months ago
  7. OpenSessame Group Title
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    |dw:1377490733250:dw|

    • 11 months ago
  8. mathstudent55 Group Title
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    |dw:1377490731812:dw|

    • 11 months ago
  9. OpenSessame Group Title
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    Alright to do that you just add and divide right?

    • 11 months ago
  10. OpenSessame Group Title
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    Like the Xs and the Ys respectively?

    • 11 months ago
  11. mathstudent55 Group Title
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    Right. Add each 2 x's and divide by 2. Add each 2 y's and divide by 2.

    • 11 months ago
  12. OpenSessame Group Title
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    Okay, easier then it sounds!

    • 11 months ago
  13. mathstudent55 Group Title
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    Now we need to see what the quadrilateral made by connecting midpoints is.

    • 11 months ago
  14. OpenSessame Group Title
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    A rhombus!

    • 11 months ago
  15. mathstudent55 Group Title
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    |dw:1377491112017:dw|

    • 11 months ago
  16. OpenSessame Group Title
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    Then is you them into right triangles you find that it is a square?

    • 11 months ago
  17. mathstudent55 Group Title
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    |dw:1377491168215:dw|

    • 11 months ago
  18. OpenSessame Group Title
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    YEA:)

    • 11 months ago
  19. mathstudent55 Group Title
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    Notice that every side of the new quadrilateral is the hypotenuse of a triangle with both legs measuring 2. Therefore, all sides of the quadrilateral are congruent, and the quadrilateral is a rhombus.

    • 11 months ago
  20. mathstudent55 Group Title
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    The next question is if the rhombus is also a square.

    • 11 months ago
  21. mathstudent55 Group Title
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    All we need to do is to see if any two consecutive sides are perpendicular.

    • 11 months ago
  22. OpenSessame Group Title
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    Which they are!

    • 11 months ago
  23. mathstudent55 Group Title
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    |dw:1377491486110:dw|

    • 11 months ago
  24. mathstudent55 Group Title
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    One slope is 1. The other slope is -1. The slopes of two consecutive sides are negative reciprocals, so those two sides are perpendicular.

    • 11 months ago
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    I get it:)

    • 11 months ago
  26. mathstudent55 Group Title
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    |dw:1377491738087:dw| Opposite angles of any parallelogram are congruent.

    • 11 months ago
  27. mathstudent55 Group Title
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    Also all angles added up are 360 degrees.

    • 11 months ago
  28. mathstudent55 Group Title
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    |dw:1377491805994:dw|

    • 11 months ago
  29. mathstudent55 Group Title
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    x + x + 90 + 90 = 360 x = 90 All angles measure 90 degrees, and all sides a congruent, so it's a square.

    • 11 months ago
  30. OpenSessame Group Title
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    Yup:) hey! can you go back to the first question for a second?

    • 11 months ago
  31. mathstudent55 Group Title
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    ok

    • 11 months ago
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