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.
Geometry problem solving
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 illstructured 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? Mind Map Help. To see a note: Hover over a yellow note button. To Fold/Unfold: click a branch. To Pan: click and drag the map canvas.
Problem Solving. Activate Flash plugin or
Javascript and reload to view the Mind Map of How to Solve It,
Interactive Mind Map, Elearning.

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