Dynamic Geometry Problem 1463: Parallelogram, Interior Point, Opposite Triangles with Equal Sum of Areas.

Let ABCD be a parallelogram with a point P inside ABCD (see the figure below). If S1 = Area APB, S3 = Area CPD, S2 = Area BPC, and S4 = Area APD, prove that S1 + S3 = S2 + S4.


Static Diagram of Geometry Problem 1463

Dynamic Geometry Problem 1463: Parallelogram, Interior Point, Opposite Triangles with Equal Sum of Areas, Step-by-step Illustration. Using GeoGebra


Poster of Geometry Problem 1463 using iPad Apps

Poster of Problem 1463, Parallelogram, Interior Point, Opposite Triangles with Equal Sum of Areas, Step-by-step Illustration, GeoGebra, iPad

Classroom Resource:
Interactive step-by-step animation using GeoGebra

This step-by-step interactive illustration was created with GeoGebra.

  • To explore (show / hide): click/tap a check box.
  • To stop/play the animation: click/tap the icon in the lower left corner.
  • To go to first step: click/tap the "Go to step 1" button.
  • To manipulate the interactive figure: click/tap and drag the blue points or figures.

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