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Thread: Thales' theorem

  1. #1
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    Thales' theorem

    I could solve the first question but got stock in the second one. I have spent so many ours in solving the second one but with no luck. Please help.

    QUAD is a trapezoid.
    The non parallel sides [QD] and [UA] of the trapezoid are cut by a line parallel to the bases in B and C respectively.
    1) Show that QB/BD = UC/CA
    Answer:
    using Thales' theorem:
    QB/BD = QR/RA
    UC/CA = QR/RA
    Then, QB/BD = UC/CA

    2) Find a ratio equal to BC/DA (SHOW YOUR WORK)
    PLEASE help with this one!!!
    Attached Thumbnails Attached Thumbnails Thales' theorem-trapezoid.png  
    Last edited by Libraoct7; Feb 15th 2018 at 02:11 PM.
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  2. #2
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    Re: Thales' theorem

    NOT "showing my work", $\frac{BC}{DA}= \frac{QU}{BC}= \frac{QU}{DA}$. You give the reasons.
    Last edited by HallsofIvy; Feb 16th 2018 at 11:23 AM.
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  3. #3
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    Re: Thales' theorem

    Thank you for the hint.
    I still don't know how you got this answer. I have tried to find the reason for your answer but couldn't. Please, help me.

    However, this leads me to another question.
    Using your answer QU/BC = QU/DA, does this mean BC/DA = 1 always?
    Last edited by Libraoct7; Feb 19th 2018 at 02:51 PM.
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  4. #4
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    Re: Thales' theorem

    Hi, your answer, with all respect is wrong.
    in your answer you stated that QU/BC = QU/DA
    This makes BC = DA witch is impossible, since [DA] is longer than [BC].
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