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Math Help - Interesting Geometry Problem

  1. #1
    Newbie Bobby Bob's Avatar
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    Interesting Geometry Problem

    Can anybody get this Geo Quiz,

    Hint:

    You need to add some lines.
    Attached Thumbnails Attached Thumbnails Interesting Geometry Problem-geoquiz.jpg  
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  2. #2
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    Is ABCD a square or just a parallelogram?
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  3. #3
    Newbie Bobby Bob's Avatar
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    Square indeed

    Sorry, Yes it is a square.
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  4. #4
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    Here are all the relationships. Some are redundant.

    F = J
    G = N
    M = K
    S = P
    R = Q

    F + H + J = 180
    G + M + S = 180
    K + N + P = 180
    Q + R + T = 180

    H + K + M + T = 360

    F + G = 90
    J + N = 90
    R + S = 90
    P + Q = 90
    Attached Thumbnails Attached Thumbnails Interesting Geometry Problem-fghjkmnpqrst.png  
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  5. #5
    Newbie Bobby Bob's Avatar
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    Cool but could you explain how you solved for angles M K and T.
    You are not allowed to use Trig. sorry I didn't mention that earlier.
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  6. #6
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    When you draw that (green) line, with the properties of a square and an isosceles triangle, you created another isosceles triangle down there. The left triangle and the right triangle also become congruent. No trig is involved. This problem can be solved completely linearly.
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  7. #7
    Newbie Bobby Bob's Avatar
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    I still don't understand how you solved either angle M or angle T.

    Once I understand your method I'll show you the way i did it.

    Bob
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  8. #8
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    Honestly, I did not solve for any particular angles. I formed a 12-dimensional matrix with overdetermined equations, and performed gaussian elimination on it.
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  9. #9
    Junior Member theprof's Avatar
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    Quote Originally Posted by Bobby Bob
    Can anybody get this Geo Quiz,

    Hint:

    You need to add some lines.
    The answer is 60.
    Proof.
    If <ECD was not 60 then <BAE could not be 15.


    PS
    the other guy is wrong...
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  10. #10
    Newbie Bobby Bob's Avatar
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    Show your work?

    OK,

    Paul and Prof,

    Could you both post your work on how to solve this problem so that we can evaluate them both.

    Bob
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  11. #11
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    Prof is right.
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  12. #12
    Newbie Cooler's Avatar
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    Geometric proof

    These are the lines you need to add.

    Sorry it is so messy.
    Attached Thumbnails Attached Thumbnails Interesting Geometry Problem-geometric-proof.gif  
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