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 illstructured problem. By
“construction,” we mean adding geometric figures (points, lines,
planes) to a problem figure that wasn’t mentioned as "given."
