Median triangle

File:Median triangle.svg

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

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 $\frac{3}{4}$ 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 $\frac{3}{4}$.

See also

• Automedian triangle