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parallelogram law (Theorem)

Let $ABCD$ be a parallelogram with side lengths $u,v$ and whose diagonals have lengths $d_1$ and $d_2$ then

\begin{displaymath}2u^2+2v^2=d_1^2 + d_2^2.\end{displaymath}

\framebox{ \begin{pspicture*}(-1,-1)(6,3) \pspolygon(0,0)(4,0)(5,2)(1,2) \uput[2... ...ne(4,0)(1,2) \uput[0](1.7,0.5){$d_1$} \uput[0](1.8,1.5){$d_2$} \end{pspicture*}}



"parallelogram law" is owned by drini. [ owner history (1) ]
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See Also: parallelogram, quadrilateral, rectangle, square, rhombus, Apollonius theorem, median, parallelogram law


Attachments:
proof of parallelogram law (Proof) by Mathprof
alternate proof of parallelogram law (Proof) by drini
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Cross-references: diagonals, lengths, side, parallelogram
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This is version 6 of parallelogram law, born on 2001-12-11, modified 2005-01-19.
Object id is 1082, canonical name is ParallelogramLaw.
Accessed 10620 times total.

Classification:
AMS MSC: 51-00 (Geometry :: General reference works )
Pending Errata and Addenda
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