Median triangle

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 ${\displaystyle {\tfrac {3}{4}}}$ 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 ${\displaystyle {\tfrac {3}{4}}}$.^[1][2][3]

median triangle: ${\displaystyle \triangle BGF}$
reference triangle:${\displaystyle \triangle ABC}$
median triangle of the median triangle:${\displaystyle \triangle BKH}$
areas: ${\displaystyle |\triangle BGF|={\tfrac {3}{4}}|\triangle ABC|}$
similarity: ${\displaystyle \triangle BGF\sim \triangle BKH}$
ratios: ${\displaystyle {\tfrac {|BH|}{|BC|}}={\tfrac {|HK|}{|AB|}}={\tfrac {|BK|}{|AC|}}={\tfrac {3}{4}}}$

See also

• Automedian triangle