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Problem 519: Triangle, Squares, Altitude, Perpendicular, Rectangle, Area. Level: High School, College, SAT Prep.

The drawing shows a triangle ABC with the squares ABDE and BCFG and the altitude BH. If HMN and HPQ are perpendicular to BC and AB respectively, prove that the areas of the rectangles BDQP and BMNG are equal.
 

Geometry problem about triangle, square, perpendicular, rectangle, and area
 

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."

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