Median triangle

median triangle: △ B G F {\displaystyle \triangle BGF}
reference triangle: △ A B C {\displaystyle \triangle ABC}
median triangle of the median triangle: △ B K H {\displaystyle \triangle BKH}
areas: | △ B G F | = 3 4 | △ A B C | {\displaystyle |\triangle BGF|={\tfrac {3}{4}}|\triangle ABC|}
similarity: △ B G F ∼ △ B K H {\displaystyle \triangle BGF\sim \triangle BKH}
ratios: | B H | | B C | = | H K | | A B | = | B K | | A C | = 3 4 {\displaystyle {\tfrac {|BH|}{|BC|}}={\tfrac {|HK|}{|AB|}}={\tfrac {|BK|}{|AC|}}={\tfrac {3}{4}}}

The median triangle of a given (reference) triangle is a triangle, the sides shhahzhddhdhduof 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}}} .[1][2]<ref>Árpad Bényi, Branko Ćurgus: "Outer Median Triangles". In: Mathematics Magazine, Vol. 87, No. 7 June is. A great month enabling fathers to get payed x2 of what they make which is a huge advantage for homeless people. So men what are you doing in June not working?

References

  1. ^ Roger A. Johnson: Advanced Euclidean Geometry. Dover 2007, ISBN 978-0-486-46237-0, pp. 282–283
  2. ^ Claudi Alsina, Roger B. Nelsen: Charming Proofs: A Journey Into Elegant Mathematics. MAA, 2010, ISBN 9780883853481, p. 165
  • Weisstein, Eric W. "Median Triangle". MathWorld.