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Math Help - isoscels trapezium

  1. #1
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    isoscels trapezium

    prove that in an isosceles trapezium
    [sum of parallel sides] x [sum of non parallel sides]= product of diagnols
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  2. #2
    Super Member Bacterius's Avatar
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    A isosceles trapezium named ABCD has just been created from nothing. The sides (AB) and (CD) are parallel. Therefore, we have :

    (AB + CD)(BC + AD) = AC \times BD

    Note that BC = AD (since the trapezium is isosceles)
    Therefore :

    (AB + CD)(2BC) = AC \times BD

    Now draw such a trapezium and think of as many useful things as you can : Thales, Pythagoras, Trigonometry, Vectors, anything. Then try putting it all together to substitute formulas into the original equation, so as to prove that the sum of the parallel sides times the sum of the non-parallel sides equals the product of the diagonals. Does it help ?
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  3. #3
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    sorry,I am not able to understand
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  4. #4
    Super Member Bacterius's Avatar
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    What don't you understand ?
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  5. #5
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    what do you mean to say?
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  6. #6
    Super Member Bacterius's Avatar
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    Quote Originally Posted by jashansinghal View Post
    what do you mean to say?
    I'm trying to give you a hint on how to do it. I won't do it for you.
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  7. #7
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    please help me
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  8. #8
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    Quote Originally Posted by jashansinghal View Post
    prove that in an isosceles trapezium
    [sum of parallel sides] x [sum of non parallel sides]= product of diagnols
    Shouldn't that be:
    [product of parallel sides] + [product of non parallel sides] = product of diagonals

    In other words, if d = diagonal, a and b = parallel sides, c = non parallel sides:
    prove that d^2 = ab + c^2
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  9. #9
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    ya...it should be this...but how to proceed
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  10. #10
    Super Member Bacterius's Avatar
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    Quote Originally Posted by jashansinghal View Post
    ya...it should be this...but how to proceed
    Wait wait ... can you give the exact terms of the question ? Otherwise it's useless.
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  11. #11
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    prove that in an isosceles trapezium
    [sum of parallel sides] x [sum of non parallel sides]= product of diagnols
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  12. #12
    Super Member Bacterius's Avatar
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    Quote Originally Posted by jashansinghal View Post
    prove that in an isosceles trapezium
    [sum of parallel sides] x [sum of non parallel sides]= product of diagnols
    Are you just solving for solving or what ?
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  13. #13
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    please help me....can you do first few steps
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  14. #14
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    stated
    Quote Originally Posted by jashansinghal View Post
    prove that in an isosceles trapezium
    [sum of parallel sides] x [sum of non parallel sides]= product of diagnols
    asked for clarification
    Quote Originally Posted by Bacterius View Post
    Wait wait ... can you give the exact terms of the question ?
    restated
    Quote Originally Posted by jashansinghal View Post
    prove that in an isosceles trapezium
    [sum of parallel sides] x [sum of non parallel sides]= product of diagnols
    ...
    a counterexample:
    Attached Thumbnails Attached Thumbnails isoscels trapezium-cyclicquadrilateral.jpg  
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