median triangle

File:Median triangle.svg

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 $\backslash tfrac\{3\}\{4\}$ 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 $\backslash tfrac\{3\}\{4\}$.Roger A. Johnson: Advanced Euclidean Geometry. Dover 2007, {{ISBN|978-0-486-46237-0}}, pp. 282–283Claudi Alsina, Roger B. Nelsen: Charming Proofs: A Journey Into Elegant Mathematics. MAA, 2010, {{ISBN|9780883853481}}, p. 165Árpad Bényi, Branko Ćurgus: "Outer Median Triangles". In: Mathematics Magazine, Vol. 87, No. 3 (June 2014), pp. 185–194 ([https://www.jstor.org/stable/pdf/10.4169/math.mag.87.3.185.pdf JSTOR])