Quantcast

A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

OpenSessame

  • 2 years 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?

  • This Question is Closed
  1. OpenSessame
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    |dw:1377490333537:dw|

  2. mathstudent55
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I just made it a bit bigger. |dw:1377490546842:dw|

  3. mathstudent55
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1377490654352:dw|

  4. OpenSessame
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    So I know the answer is, The rhombus is a square but i need help finding midpoints.

  5. mathstudent55
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    We can label all midpoints.

  6. OpenSessame
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Im guessing|dw:1377490680684:dw|

  7. OpenSessame
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    |dw:1377490733250:dw|

  8. mathstudent55
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1377490731812:dw|

  9. OpenSessame
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Alright to do that you just add and divide right?

  10. OpenSessame
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Like the Xs and the Ys respectively?

  11. mathstudent55
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Right. Add each 2 x's and divide by 2. Add each 2 y's and divide by 2.

  12. OpenSessame
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Okay, easier then it sounds!

  13. mathstudent55
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Now we need to see what the quadrilateral made by connecting midpoints is.

  14. OpenSessame
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    A rhombus!

  15. mathstudent55
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1377491112017:dw|

  16. OpenSessame
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Then is you them into right triangles you find that it is a square?

  17. mathstudent55
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1377491168215:dw|

  18. OpenSessame
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    YEA:)

  19. mathstudent55
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    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
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    The next question is if the rhombus is also a square.

  21. mathstudent55
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    All we need to do is to see if any two consecutive sides are perpendicular.

  22. OpenSessame
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Which they are!

  23. mathstudent55
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1377491486110:dw|

  24. mathstudent55
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    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
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I get it:)

  26. mathstudent55
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1377491738087:dw| Opposite angles of any parallelogram are congruent.

  27. mathstudent55
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Also all angles added up are 360 degrees.

  28. mathstudent55
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1377491805994:dw|

  29. mathstudent55
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    x + x + 90 + 90 = 360 x = 90 All angles measure 90 degrees, and all sides a congruent, so it's a square.

  30. OpenSessame
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Yup:) hey! can you go back to the first question for a second?

  31. mathstudent55
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ok

  32. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.