proof of parallelogram law

The proof follows directly from Apollonius theoremMathworldPlanetmath noticing that each diagonal is a median for the triangles in which parallelogramMathworldPlanetmath is split by the other diagonal. Also, the diagonals bisect each other.

Therefore, Apollonius theorem implies


Multiplying both sides by 2 and simplification leads to the desired expression.

Title proof of parallelogram lawPlanetmathPlanetmath
Canonical name ProofOfParallelogramLaw
Date of creation 2013-03-22 12:41:29
Last modified on 2013-03-22 12:41:29
Owner Mathprof (13753)
Last modified by Mathprof (13753)
Numerical id 5
Author Mathprof (13753)
Entry type Proof
Classification msc 51-00
Related topic ApolloniusTheorem
Related topic Median
Related topic ProofOfParallelogramLaw2