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 S1 = area AEPH, S2 = area PEBF, S3 = area PFCG and S4 = area PGDH, prove that S1 + S3 = S2 + S4.


Static Diagram of Geometry Problem 1464

Poster of Problem 1464, Quadrilateral, Interior Point, Midpoint of Sides, Equal Sum of Areas, Step-by-step Illustration, GeoGebra, iPad


Poster of Geometry Problem 1464 using iPad Apps

Poster of Problem 1464, Quadrilateral, Interior Point, Midpoint of Sides, 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.

GeoGebra is free and multi-platform dynamic mathematics software for all levels of education that joins geometry, algebra, tables, graphing, statistics and calculus application, intended for teachers and students. Many parts of GeoGebra have been ported to HTML5.

Recent Additions

Geometry Problems
Open Problems
Visual Index
Ten problems: 1411-1420
All Problems
Triangle
Area
Triangle Area
Quadrilateral
Midpoint
Dynamic Geometry
GeoGebra
HTML5 and Dynamic Geometry
iPad Apps
View or Post a solution