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Online Geometry Problem 869: Triangle, Median, Three Equilateral Triangles, Collinear Points, Midpoint. Level: High School, College, Mathematics Education

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 869: Triangle, Median, Three Equilateral Triangles, Collinear Points, Midpoint
 


 

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." 

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