Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

alwaysdancing18

  • 3 years ago

Can you conclude that the quadrilateral is a parallelogram? Explain.

  • This Question is Closed
  1. alwaysdancing18
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1355467239515:dw|

  2. Dido525
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    OOps.

  3. Dido525
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1355456638221:dw|

  4. Dido525
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Lets use a geometric argument.

  5. alwaysdancing18
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ok....

  6. Dido525
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    If we draw a line such it it intersects two sides.

  7. Dido525
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Since the lengths on the opposite sides are the same, according to the parallel lines theorem, angle a must equal angle d.

  8. Dido525
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Similarly, angle must equal angle c.

  9. Dido525
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    If we make two triangles, Triangle abc and triangle def

  10. Dido525
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    180-e-d must equal angle f.

  11. Dido525
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Are you following me so far?

  12. alwaysdancing18
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yes I am, I am writing this down

  13. Dido525
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Similarly, 180 - a -c must equal b.

  14. alwaysdancing18
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ok I dont understand what 180-a-c means

  15. Dido525
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Since a = d and c = e , therefore we can conclude f equal b.

  16. Dido525
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I mean I am subtracting going: 180 degrees - angle a - angle c.

  17. Dido525
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Because in a triangle there is 180 degrees. Do you understand or shall I explain more?

  18. alwaysdancing18
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    oh.. so does that mean 180 degrees has to be subtracted by angle a and c to find B? or am I completely wrong?

  19. Dido525
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Yes you are correct but do you understand why?

  20. alwaysdancing18
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    because.... nope I got nothing... I just remember thats a rule somewhere right?

  21. Dido525
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1355457201086:dw|

  22. Dido525
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1355457242628:dw|

  23. Dido525
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Does that make sense?

  24. alwaysdancing18
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    so that means both ABC and DEF are equal because they were cut equally in half. So each triangle equal 180 and both together is 360?

  25. Dido525
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yeah okay, you could reason it that way too :P . But you had to prove they were equal first ;) .

  26. alwaysdancing18
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    SAS?

  27. Dido525
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    You can only prove they are equal if you cut the quadrilateral in half like I said. THen you had to prove that I did cut it in half by proving all the angles were the same.

  28. Dido525
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Ohh yeah, that's valid too :) .

  29. Dido525
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Good! :) .

  30. alwaysdancing18
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    so to answer the question how do I conclude its a parallelogram?

  31. Dido525
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Now since you have proved all the angles are the same on opposite sides, you can conclude that this quadrilateral in indeed a parralelogram because the opposite sides have the same length and the angles on opposite sides of each other are the same as well.

  32. alwaysdancing18
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Thank you so much for that. You were very patient and kind. I will remember this!! Thanks. :D

  33. Dido525
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    You are welcome :) .

  34. 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