Triangle Quadrangle Puzzle

This is another simple problem from Five Hundred Mathematical Challenges:

“Problem 57.  Let X be any point between B and C on the side BC of the convex quadrilateral ABCD (as in the Figure).  A line is drawn through B parallel to AX and another line is drawn through C parallel to DX.  These two lines intersect at P.  Prove that the area of the triangle APD is equal to the area of the quadrilateral ABCD.”

See the Triangle Quadrangle Puzzle

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