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Math Help - parallelogram-how to prove

  1. #1
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    Thumbs up parallelogram-how to prove

    parallelogram-how to prove-att-jpg.jpg
    Given: ABCD - parallelogram
    BE=DM
    How to prove:
    a)ED=MB
    b)BEDM-parallelogram ?
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  2. #2
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    Re: parallelogram-how to prove

    Quote Originally Posted by nataku View Post
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    Given: ABCD - parallelogram
    BE=DM
    How to prove:
    a)ED=MB
    b)BEDM-parallelogram ?
    You can show that EA and CM are equal. You know BC and AD are equal and that A=C. That gets you BMC and EAD being congruent and thus BM=ED.

    There's a proof that if one pair of opposite sides of a quadrilateral is both parallel (BE and MD are parallel because ABCD is a parallelogram) and congruent, (just proved), that the quadrilateral is a parallelogram here at the bottom of the page.
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  3. #3
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    Re: parallelogram-how to prove

    Quote Originally Posted by nataku View Post
    Click image for larger version. 

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    Given: ABCD - parallelogram
    BE=DM
    How to prove:
    a)ED=MB b)BEDM-parallelogram ?
    You might just notice that $m(BE)=m(MD)~\&~BE\|MD$ (two parallel sides of equal length).
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  4. #4
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    Re: parallelogram-how to prove

    Quote Originally Posted by romsek View Post
    You can show that EA and CM are equal. You know BC and AD are equal and that A=C. That gets you BMC and EAD being congruent and thus BM=ED.

    There's a proof that if one pair of opposite sides of a quadrilateral is both parallel (BE and MD are parallel because ABCD is a parallelogram) and congruent, (just proved), that the quadrilateral is a parallelogram here at the bottom of the page.
    If both pairs of opposite sides of a quad are congruent then the quad is a parrelogram
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