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Math Help - Basic geometry proof

  1. #1
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    Basic geometry proof

    Given a triangle ABC and D is the midpoint of BC. Prove that

    (a) AD < (AB+AC)/2

    (b) AD > (AB+AC-BC)/2
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  2. #2
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    Re: Basic geometry proof

    Quote Originally Posted by MichaelLight View Post
    Given a triangle ABC and D is the midpoint of BC. Prove that
    (a) AD < (AB+AC)/2
    (b) AD > (AB+AC-BC)/2
    Using vectors this is rather easy.
    \overrightarrow {DA}  = \overrightarrow {AB}  + \overrightarrow {BD} \;\& \,\overrightarrow {DA}  = \overrightarrow {AC}  + \overrightarrow {CD}
    Note that \overrightarrow {BD}+\overrightarrow {CD}=0.

    Use the triangle inequality.
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