Median triangle explained

The median triangle of a given (reference) triangle is a triangle, the sides of which are equal and parallel to the medians of its reference triangle. The area of the median triangle is

\tfrac{ 3 }{ 4 } of the area of its reference triangle, and the median triangle of the median triangle is similar to the reference triangle of the first median triangle with a scaling factor of \tfrac{ 3 }{ 4 } .^{[1] [2] [3]}

Notes and References

1. Roger A. Johnson: Advanced Euclidean Geometry. Dover 2007,, pp. 282–283
2. Claudi Alsina, Roger B. Nelsen: Charming Proofs: A Journey Into Elegant Mathematics. MAA, 2010,, p. 165
3. Árpad Bényi, Branko Ćurgus: "Outer Median Triangles". In: Mathematics Magazine, Vol. 87, No. 3 (June 2014), pp. 185–194 (JSTOR)