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Math Help - Trapezoid Problem

  1. #1
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    Trapezoid Problem

    Given trapezoid ABCD with diagonals intersecting in X, find three pairs of triangles with equal areas.



    How would one go about doing and proving that?
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  2. #2
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    Quote Originally Posted by Kolbeck10 View Post
    Given trapezoid ABCD with diagonals intersecting in X, find three pairs of triangles with equal areas.



    How would one go about doing and proving that?
    ABD and ABC have equal base (AB) and altitude and hence equal area.

    CDB and CDA for the same reason have equal area.

    AXD and BXC, as ABD and ABC have the same area and:

    area(ABD)=area(AXD)+area(AXB)

    area(ABC)=area(BXC)+area(AXB).

    RonL
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  3. #3
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    Quote Originally Posted by CaptainBlack View Post
    ABD and ABC have equal base (AB) and altitude and hence equal area.

    CDB and CDA for the same reason have equal area.

    AXD and BXC, as ABD and ABC have the same area and:

    area(ABD)=area(AXD)+area(AXB)

    area(ABC)=area(BXC)+area(AXB).

    RonL
    Is this dependent on the fact that it's an isosceles trapezoid, or would it be that way for one where the two non-parallel sides aren't the same?
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by Kolbeck10 View Post
    Is this dependent on the fact that it's an isosceles trapezoid, or would it be that way for one where the two non-parallel sides aren't the same?
    No, I tried to ignore that aspect of the diagram.

    RonL
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  5. #5
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    Quote Originally Posted by CaptainBlack View Post
    No, I tried to ignore that aspect of the diagram.

    RonL
    Alright, perfect, thanks for the help.
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