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Median triangle
Mathematical concept

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 3 4 {\displaystyle {\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 3 4 {\displaystyle {\tfrac {3}{4}}} .

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See also

References

  1. Roger A. Johnson: Advanced Euclidean Geometry. Dover 2007, ISBN 978-0-486-46237-0, pp. 282–283 /wiki/ISBN_(identifier)

  2. Claudi Alsina, Roger B. Nelsen: Charming Proofs: A Journey Into Elegant Mathematics. MAA, 2010, ISBN 9780883853481, p. 165 /wiki/ISBN_(identifier)

  3. Árpad Bényi, Branko Ćurgus: "Outer Median Triangles". In: Mathematics Magazine, Vol. 87, No. 3 (June 2014), pp. 185–194 (JSTOR) https://www.jstor.org/stable/pdf/10.4169/math.mag.87.3.185.pdf