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Math Help - a rectangle must be square

  1. #1
    rcs
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    Senior Member rcs's Avatar
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    a rectangle must be square

    I'm not really really good in geometry sorry need your help.

    The points P
    (0,0) , Q(a,0), R(a,b), S(0,b) are the vertices of the rectangle. Show that if the diagonals meet at right angles, then a = b and the rectangle must be a square.

    Thanks.
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    \overrightarrow{PR}\perp \overrightarrow{QS}\Leftrightarrow\overrightarrow{  PR}\cdot \overrightarrow{QS}\Leftrightarrow \ldots \Leftrightarrow -a^2+b^2=0

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