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OpenSessame

  • one year ago

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?

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  1. OpenSessame
    • one year ago
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    |dw:1377490333537:dw|

  2. mathstudent55
    • one year ago
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    I just made it a bit bigger. |dw:1377490546842:dw|

  3. mathstudent55
    • one year ago
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    |dw:1377490654352:dw|

  4. OpenSessame
    • one year ago
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    So I know the answer is, The rhombus is a square but i need help finding midpoints.

  5. mathstudent55
    • one year ago
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    We can label all midpoints.

  6. OpenSessame
    • one year ago
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    Im guessing|dw:1377490680684:dw|

  7. OpenSessame
    • one year ago
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    |dw:1377490733250:dw|

  8. mathstudent55
    • one year ago
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    |dw:1377490731812:dw|

  9. OpenSessame
    • one year ago
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    Alright to do that you just add and divide right?

  10. OpenSessame
    • one year ago
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    Like the Xs and the Ys respectively?

  11. mathstudent55
    • one year ago
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    Right. Add each 2 x's and divide by 2. Add each 2 y's and divide by 2.

  12. OpenSessame
    • one year ago
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    Okay, easier then it sounds!

  13. mathstudent55
    • one year ago
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    Now we need to see what the quadrilateral made by connecting midpoints is.

  14. OpenSessame
    • one year ago
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    A rhombus!

  15. mathstudent55
    • one year ago
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    |dw:1377491112017:dw|

  16. OpenSessame
    • one year ago
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    Then is you them into right triangles you find that it is a square?

  17. mathstudent55
    • one year ago
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    |dw:1377491168215:dw|

  18. OpenSessame
    • one year ago
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    YEA:)

  19. mathstudent55
    • one year ago
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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.

  20. mathstudent55
    • one year ago
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    The next question is if the rhombus is also a square.

  21. mathstudent55
    • one year ago
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    All we need to do is to see if any two consecutive sides are perpendicular.

  22. OpenSessame
    • one year ago
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    Which they are!

  23. mathstudent55
    • one year ago
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    |dw:1377491486110:dw|

  24. mathstudent55
    • one year ago
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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.

  25. OpenSessame
    • one year ago
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    I get it:)

  26. mathstudent55
    • one year ago
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    |dw:1377491738087:dw| Opposite angles of any parallelogram are congruent.

  27. mathstudent55
    • one year ago
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    Also all angles added up are 360 degrees.

  28. mathstudent55
    • one year ago
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    |dw:1377491805994:dw|

  29. mathstudent55
    • one year ago
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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.

  30. OpenSessame
    • one year ago
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    Yup:) hey! can you go back to the first question for a second?

  31. mathstudent55
    • one year ago
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    ok

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