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Math Help - proving angles?

  1. #1
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    proving angles?

    proving angles?-sub11-16.jpg

    In the figure above, FD || AC and EF || CB. Prove that ∠C≅∠EFD and that ∠CEF≅∠FDC.

    Can someone offer help?
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  2. #2
    Junior Member BariMutation's Avatar
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    I can't quite remember the name of the theorem, but I know it exists. Remember that the picture I attached holds true. That is essentially what is happening with both of your questions, only with parallel lines. Notice that EF is cutting through the parallel lines of FD and AC. Are you following?
    Attached Thumbnails Attached Thumbnails proving angles?-untitled.png  
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  3. #3
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    Err...yeah, I notice what its cutting through...but how does it relate to the picture you attached?
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  4. #4
    Junior Member BariMutation's Avatar
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    I just flipped the reference point, but it's still true. What about now? The red lines are, as you can guess, just the lines extended.
    Attached Thumbnails Attached Thumbnails proving angles?-untitled.png  
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  5. #5
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    Gotcha, I think I understand the picture...but how does it help me solve the problem?
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  6. #6
    Junior Member BariMutation's Avatar
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    ∠C≅∠EFD is what I actually drew in there, and ∠CEF≅∠FDC is the same theorem, just with the opposing (smaller) angles. Essentially, you just have to state the theorem and draw in what I did (at least that's what I assume you have to do. I can't imagine you have to prove the theorems too).
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  7. #7
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    Actually there is no drawing. I think what they mean by proving is by writing it out somehow. This is computer work, not a worksheet.
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  8. #8
    Junior Member BariMutation's Avatar
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    Hm... are you able to do a T proof? For instance,

    STATEMENT............THEOREM/INFORMATION
    x=y...........................given in the problem
    x=x..............................substitution
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  9. #9
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    Actually im not really sure. Novelstars--the website where I do my work on is a bit iffy when explaining things. If it helps I think the theorm is triangle sum theorem.
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  10. #10
    Junior Member BariMutation's Avatar
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    Well, if you're just turning in a typed paper, then use the T proof I showed you. However, if you have to enter your answer in a dialog line and press "OK" or something, I'd just say the theorems you used... are you able to take a screen shot of what you're seeing on the site?
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  11. #11
    MHF Contributor Unknown008's Avatar
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    The ones you used are the alternate (or Z) angles and the opposite angles

    This should be easy now. You can proove \angle C \equiv \angle EFD directly from what BariMutation told you.

    And using the fact that CDFE is a rhombus (or using the parallel lines again), you will see that \angle CEF\equiv\angle FDC.
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