Geometry Problem: Machu Picchu Inca Trail

 Problem 251. Parallelogram, sides, diagonals, squares, areas

The figure shows a parallelogram ABCD. If squares of area S1, S2, S3, and S4 are constructed on the sides and diagonals, prove that 2S1 + 2S2 = S3 + S4 .

Problem about parallelogram with diagonals and squares areas
 

See also: 

  Median length, Apollonius' Theorem
  Pythagoras Theorem
  Euclid's Elements Book II Proposition 13
  Stewart Theorem 

 

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