Home Geometry Problems All Problems Parallelogram Area of a Parallelogram 481-490 Solution / comment        By Antonio Gutierrez
Problem 489. Parallelogram, Triangle, Quadrilateral, Area.
Level: High School, College, SAT Prep.

The figure shows a parallelogram ABCD. E is a point on DC extended. Line EB extended meet DA extended at F. CF and AE meet at G. Prove that the area of triangle EFG is equal to the area of quadrilateral ADCG.

Illustration: Parallelogram, Triangle, Area

Geometry problem solving is one of the most challenging skills for students to learn. When a problem requires auxiliary construction, the difficulty of the problem increases drastically, perhaps because deciding which construction to make is an ill-structured problem. By “construction,” we mean adding geometric figures (points, lines, planes) to a problem figure that wasn’t mentioned as "given."

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George Pólya's 1945 book "How to Solve It, A new aspect of Mathematical Method", is a book describing methods of problem solving. It suggests the following steps when solving a mathematical problem: (1) First, you have to understand the problem. (2) After understanding, then make a plan. (3) Carry out the plan. (4) Look back on your work. How could it be better? 

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