Home Geometry Mind Map Problems All Problems 491-500 Geoboard for iPad Solution, comment        By Antonio Gutierrez
Problem 496. Triangle, Two Squares, 90 Degrees, Concurrency.
Level: High School, College, SAT Prep.

The figure shows a triangle ABC with the squares ABDE and BCFG. AG and CD meet at P. Prove that: (1) CD and AG are congruent and perpendicular. (2) CD, AG, and EF are concurrent in P. (3) EF is the angle bisector of angle GPC.
 

Triangle, Two Squares, 90 degrees
 

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."

How to Solve It, Interactive Mind Map

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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