Problem 521: Triangle, Squares, Altitude, Rectangles, Areas.
Level: High School, College, SAT Prep.
The drawing shows a triangle ABC with the squares
ABDE, BCFG, and ACJK. Lines
AMN, BHT, and CPQ are perpendicular to
BC, AC, and AB respectively. Prove that the areas of the rectangles S1
are equal, S2
are equal, and S3
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."