Parallelogram

This is a discussion on Parallelogram within the A Brief History of Cprogramming.com forums, part of the Community Boards category; Hey, guys, I need a little help with this extra credit problem... How do you prove the diagonals of a ...

  1. #1
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    Parallelogram

    Hey, guys, I need a little help with this extra credit problem...

    How do you prove the diagonals of a parallelogram are perpendicular to each other, meaning that the diagonals' slopes are negative reciprocal of each other.

    And prove the diagonals bisect each other, having the same midpoint?

  2. #2
    Lead Moderator kermi3's Avatar
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    Well...you shouldn't be getting help on a graded assignment to start. But I would look at what happens when you drop an altitude.
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    There are 4 coordinates: A = (0,b), B = (-c, 0), C = (a+c,b) D = (a,0)

    I tried to find the slopes of diagonal lines AB and BC, but they're not negative reciprocal to each other.

  4. #4
    Green Member Cshot's Avatar
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    That's because AB and BC are not diagonals. AD and BC are. Heheh draw it out man
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  5. #5
    Lead Moderator kermi3's Avatar
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    Drop an altitude between the parrallel sides at a 90 degree angle. Do it on your own from there.
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    Sorry, guys. I mistyped, not lines AB and BC, but diagonal lines AD and BC. The problem is that I can't really find the slope of BC.

    slope of AD = (0 - b) / (a - 0)
    = -b/a

    slope of BC = (b - 0) / ((a+c) - -c)
    = b / a + 2c ?

    Aren't the two slopes supposed to be negative recripocal of each others?

  7. #7
    Lead Moderator kermi3's Avatar
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    Look, I'm not going to help you at all anymore....But here's a suggestion...

    Do your own work. It's graded, for credit? Don't you think it's cheating to be asking for help?
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  8. #8
    Much older and wiser Fountain's Avatar
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    well, it could show initiative
    Such is life.

  9. #9
    Lead Moderator kermi3's Avatar
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    You're right it could. However, I think that most teachers would see it as cheating. If it's graded you should do your own work and be proud of it....My opinion...I'm not closing the thread or anything, everyone must make their own choices.
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  10. #10
    Green Member Cshot's Avatar
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    If you can prove they are perpendicular, please let me know
    Try not.
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  11. #11
    Green Member Cshot's Avatar
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    hint hint
    Attached Images Attached Images  
    Try not.
    Do or do not.
    There is no try.

    - Master Yoda

  12. #12
    Lead Moderator kermi3's Avatar
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    They aren't parrallel there...he means a parallelogram:
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  13. #13
    Microsoft. Who? MethodMan's Avatar
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    Dont know if this will help but:

    From the red lines, if you know they are parallel, then the angles are the same according to the Z pattern.
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  14. #14
    Green Member Cshot's Avatar
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    Yes it is. A rectangle is a special kind of parallelogram.
    Parallelogram

    A quadrilateral whose opposite sides are parallel
    The opposite sides of a parallelogram are parallel.
    A diagonal of a parallelogram divides it into two congruent triangles.
    The opposite sides of a parallelogram are congruent.
    The opposite angles of a parallelogram are congruent.
    The consecutive angels of a parallelogram are supplementary.
    The diagonals of a parallelogram bisect each other.
    Five ways to prove a quadrilateral is a Parallelogram
    1. A quadrilateral is a parallelogram if its opposite sides are parallel.
    2. A quadrilateral is a parallelogram if its opposite sides are congruent.
    3. A quadrilateral is a parallelogram if two sides are congruent and parallel.
    4. A quadrilateral is a parallelogram if its opposite angles are congruent.
    5. A quadrilateral is a parallelogram if its diagonals bisect each other.

    Rectangle
    An equiangular parallelogram
    Rhombus
    An equilateral parallelogram
    Square
    An equilateral and equiangular parallelogram
    Try not.
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    There is no try.

    - Master Yoda

  15. #15
    Lead Moderator kermi3's Avatar
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    Bah you win Cshot. But when proving a therom like this you shouldn't use a "special kind". You should use the most generic you have.
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