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 ill-structured problem. By “construction,” we mean adding geometric figures (points, lines, planes) to a problem figure that wasn’t mentioned as "given."