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Problem 520: Triangle, Six Squares, Areas, Ratio.
Level: High School, College, SAT Prep. The drawing shows a triangle ABC with the squares of areas S1, S2, S3,
S4, S5, and S6. Prove that the ratio between the sum of areas S4+S5+S6 , and the sum of areas S1+S2+S3 is equal to 3.
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."

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