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BIGDOG96

  • 2 years ago

Use ∆ABC to answer the question that follows. Given: ∆ABC Prove: The three medians of ∆ABC intersect at a common point. When written in the correct order, the two-column proof below describes the statements and justifications for proving the three medians of a triangle all intersect in one point. Which is the most logical order of statements and justifications I, II, III, and IV to complete the proof?

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  1. BIGDOG96
    • 2 years ago
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    Statements Justifications Point F is a midpoint of Line segment AB Point E is a midpoint of Line segment AC Draw Line segment BE Draw Line segment FC by Construction Point G is the point of intersection between Line segment BE and Line segment FC Intersecting Lines Postulate Draw Line segment AG by Construction Point D is the point of intersection between Line segment AG and Line segment BC Intersecting Lines Postulate Point H lies on Line segment AG such that Line segment AG ≅ Line segment GH by Construction I BGCH is a parallelogram Properties of a Parallelogram (opposite sides are parallel) II Line segment FG is parallel to line segment BH and Line segment GE is parallel to line segment HC Midsegment Theorem III Line segment BD ≅ Line segment DC Properties of a Parallelogram (diagonals bisect each other) IV Line segment GC is parallel to line segment BH and Line segment BG is parallel to line segment HC Substitution Line segment AD is a median Definition of a Median

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  2. BIGDOG96
    • 2 years ago
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    IV, II, III, I II, IV, I, III IV, II, I, III II, IV, III, I

  3. BIGDOG96
    • 2 years ago
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    It won't let me post the statements and justification in a two column

  4. ganeshie8
    • 2 years ago
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    try taking a screenshot and post the pix... here you're trying to use parallelogram properties i think

  5. BIGDOG96
    • 2 years ago
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    I just did.

  6. BIGDOG96
    • 2 years ago
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    Does this work?

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  7. ganeshie8
    • 2 years ago
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    look at \(\triangle ABH\)

  8. BIGDOG96
    • 2 years ago
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    Just heads up I HAVE NO CLUE what I'm doing.

  9. ganeshie8
    • 2 years ago
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    FG is the midsegment , so it is parallel to BH FG || BH

  10. BIGDOG96
    • 2 years ago
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    ok

  11. ganeshie8
    • 2 years ago
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    its okay im sure you would get enough clue by the time we finish ;p

  12. BIGDOG96
    • 2 years ago
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    Alright, continue.

  13. ganeshie8
    • 2 years ago
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    do the same thing for another triangle, look at \(\triangle\) AHC whats the midsegment in that triangle

  14. BIGDOG96
    • 2 years ago
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    EB

  15. BIGDOG96
    • 2 years ago
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    ?

  16. BIGDOG96
    • 2 years ago
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    No EG?

  17. ganeshie8
    • 2 years ago
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    |dw:1347462588707:dw|

  18. ganeshie8
    • 2 years ago
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    |dw:1347462742317:dw|

  19. ganeshie8
    • 2 years ago
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    thats right, EG is the midsegment

  20. ganeshie8
    • 2 years ago
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    so EG || HC

  21. BIGDOG96
    • 2 years ago
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    Yay

  22. ganeshie8
    • 2 years ago
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    good work :) so far. so our first statement must be which one ?

  23. BIGDOG96
    • 2 years ago
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    2?

  24. ganeshie8
    • 2 years ago
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    Perfect !

  25. ganeshie8
    • 2 years ago
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    lets continue our logic from this point

  26. BIGDOG96
    • 2 years ago
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    There's only two that start with two.

  27. ganeshie8
    • 2 years ago
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    only one of them is true

  28. BIGDOG96
    • 2 years ago
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    And they both have four next

  29. ganeshie8
    • 2 years ago
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    we have this so far : we got two parallel sides according to midsegment theorem : FG || BH GE || HC

  30. ganeshie8
    • 2 years ago
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    |dw:1347463059283:dw|

  31. ganeshie8
    • 2 years ago
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    since GE || HC, BG also parallel to HC BG || HC so next statement is IV as you said

  32. ganeshie8
    • 2 years ago
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    what could be the next ?

  33. BIGDOG96
    • 2 years ago
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    1?

  34. ganeshie8
    • 2 years ago
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    |dw:1347463185726:dw|

  35. ganeshie8
    • 2 years ago
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    thats one set of parallel sides

  36. BIGDOG96
    • 2 years ago
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    Oh so 3?

  37. ganeshie8
    • 2 years ago
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    |dw:1347463228999:dw|

  38. ganeshie8
    • 2 years ago
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    thats another set of parallel sides

  39. ganeshie8
    • 2 years ago
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    doesnt it make that piece a parallelogram ?

  40. BIGDOG96
    • 2 years ago
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    Yes

  41. BIGDOG96
    • 2 years ago
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    So I was right, it's 1?

  42. ganeshie8
    • 2 years ago
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    yes ofcourse you're right :)

  43. BIGDOG96
    • 2 years ago
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    Thanks

  44. ganeshie8
    • 2 years ago
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    np.. yw ! (:

  45. BIGDOG96
    • 2 years ago
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    D

  46. BIGDOG96
    • 2 years ago
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    See you later. Thanks again!

  47. ganeshie8
    • 2 years ago
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    is that a smiley D or you're saying the correct sequence is D lol

  48. ganeshie8
    • 2 years ago
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    the correct sequence of statements is this : II, IV, I, III

  49. BIGDOG96
    • 2 years ago
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    BOTH

  50. ganeshie8
    • 2 years ago
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    hmm

  51. BIGDOG96
    • 2 years ago
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    LOL

  52. ganeshie8
    • 2 years ago
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    good luck wid ur geometry proofs looks like you're at end of course. wish u best grades :) cya

  53. BIGDOG96
    • 2 years ago
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    YEP thanks

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