Online Geometry Problem 514: Triangle, Five Squares, Line, Area. Level: High School, SAT Prep, College, Mathematics Education

The drawing shows the squares of area A₁, A₂, A₃, A₄, and A_5.  Prove that the area of triangle A equals A₃.

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.