# Dynamic Geometry Problem 1464: Quadrilateral, Interior Point, Midpoint of
Sides,
Equal Sum of Areas.

Let ABCD be a quadrilateral with a point P inside
ABCD (see the figure below). if S_{1} = area AEPH, S_{2} = area PEBF, S_{3} = area PFCG and S_{4} = area PGDH,
prove that S_{1} + S_{3} = S_{2} + S_{4}.

See solution below

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