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Math Help - Vector Proof Problem

  1. #1
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    Vector Proof Problem

    Please help with this vector proof!

    'Let ABCD be a quadrilateral in the plane, and let P and Q be the midpoints of of the sides AB and CD respectively. Show that:

    2PQ = AD + BC'

    I'm just not sure how to go about it. Thanks in advance for any help.
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  2. #2
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    Quote Originally Posted by AlanC877 View Post
    Let ABCD be a quadrilateral in the plane, and let P and Q be the midpoints of of the sides AB and CD respectively. Show that: 2PQ = AD + BC'
    \[\frac{1}{2}\overrightarrow {AB}  + \overrightarrow {BC}  + \frac{1}{2}\overrightarrow {CD}  = \overrightarrow {QP}

     - \frac{1}{2}\overrightarrow {AB}  + \overrightarrow {AD}  - \frac{1}{2}\overrightarrow {CD}  = \overrightarrow {QP}

    Now add those together.
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  3. #3
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    Thanks very much, now I realise just how easy the question actually was!
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