The figure below shows a triangle ABC with
the median BN. If ABDE, BFGN, and BHMC are squares of centers O_{1}, O_{2}, and O_{3}, respectively, prove
that (1) F is the midpoint of DH, (2) G is the midpoint of EM, (3) O_{2},
is the midpoint of O_{1}O_{3}.
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."
