The figure below shows a triangle ABC with
the median BN. If ABDE, BFGN, and BHMC are squares of centers O1, O2, and O3, respectively, prove
that (1) F is the midpoint of DH, (2) G is the midpoint of EM, (3) O2,
is the midpoint of O1O3.
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."