Geometry Problem 1381: Parallelogram, Exterior Point, Triangle, Area

Proposition

The figure below shows a parallelogram ABCD of area S with an exterior point E. If S1, S2, S3, and S4, are the areas of triangles EAB, EBC, ECD, and EAD, respectively, prove that S1 + S3 = S4 - S2 = S/2. 
 

Geometry Problem 1381: Parallelogram, Exterior Point, Triangle, Area
 

See also
Poster of Problem 1381
Conformal Mapping or Transformation of Problem 1381

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