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alwaysdancing18

  • 2 years ago

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

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  1. alwaysdancing18
    • 2 years ago
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    |dw:1355467239515:dw|

  2. Dido525
    • 2 years ago
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    OOps.

  3. Dido525
    • 2 years ago
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    |dw:1355456638221:dw|

  4. Dido525
    • 2 years ago
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    Lets use a geometric argument.

  5. alwaysdancing18
    • 2 years ago
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    ok....

  6. Dido525
    • 2 years ago
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    If we draw a line such it it intersects two sides.

  7. Dido525
    • 2 years ago
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    Since the lengths on the opposite sides are the same, according to the parallel lines theorem, angle a must equal angle d.

  8. Dido525
    • 2 years ago
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    Similarly, angle must equal angle c.

  9. Dido525
    • 2 years ago
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    If we make two triangles, Triangle abc and triangle def

  10. Dido525
    • 2 years ago
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    180-e-d must equal angle f.

  11. Dido525
    • 2 years ago
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    Are you following me so far?

  12. alwaysdancing18
    • 2 years ago
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    yes I am, I am writing this down

  13. Dido525
    • 2 years ago
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    Similarly, 180 - a -c must equal b.

  14. alwaysdancing18
    • 2 years ago
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    ok I dont understand what 180-a-c means

  15. Dido525
    • 2 years ago
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    Since a = d and c = e , therefore we can conclude f equal b.

  16. Dido525
    • 2 years ago
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    I mean I am subtracting going: 180 degrees - angle a - angle c.

  17. Dido525
    • 2 years ago
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    Because in a triangle there is 180 degrees. Do you understand or shall I explain more?

  18. alwaysdancing18
    • 2 years ago
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    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
    • 2 years ago
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    Yes you are correct but do you understand why?

  20. alwaysdancing18
    • 2 years ago
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    because.... nope I got nothing... I just remember thats a rule somewhere right?

  21. Dido525
    • 2 years ago
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    |dw:1355457201086:dw|

  22. Dido525
    • 2 years ago
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    |dw:1355457242628:dw|

  23. Dido525
    • 2 years ago
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    Does that make sense?

  24. alwaysdancing18
    • 2 years ago
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    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
    • 2 years ago
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    yeah okay, you could reason it that way too :P . But you had to prove they were equal first ;) .

  26. alwaysdancing18
    • 2 years ago
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    SAS?

  27. Dido525
    • 2 years ago
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    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
    • 2 years ago
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    Ohh yeah, that's valid too :) .

  29. Dido525
    • 2 years ago
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    Good! :) .

  30. alwaysdancing18
    • 2 years ago
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    so to answer the question how do I conclude its a parallelogram?

  31. Dido525
    • 2 years ago
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    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
    • 2 years ago
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    Thank you so much for that. You were very patient and kind. I will remember this!! Thanks. :D

  33. Dido525
    • 2 years ago
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    You are welcome :) .

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