The figure below shows a triangle ABC with
the median BM. If triangles ABD, BME, and BCF are equilateral, prove
that (1) D,E, and F are collinear; (2) E is the midpoint of DF. This entry contributed by Ajit Athle.
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."