proof of parallelogram law
The proof follows directly from Apollonius theorem noticing that each diagonal is a median for the triangles in which parallelogram is split by the other diagonal. Also, the diagonals bisect each other.
Therefore, Apollonius theorem implies
Multiplying both sides by and simplification leads to the desired expression.
|Title||proof of parallelogram law|
|Date of creation||2013-03-22 12:41:29|
|Last modified on||2013-03-22 12:41:29|
|Last modified by||Mathprof (13753)|