Median triangle

In geometry, 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 of the area of its reference triangle:

$${\displaystyle |\triangle BGF|={\frac {3}{4}}|\triangle ABC|}$$

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:

$${\displaystyle {\frac {|BH|}{|BC|}}={\frac {|HK|}{|AB|}}={\frac {|BK|}{|AC|}}={\frac {3}{4}}}$$

See also

• Automedian triangle

References

External links

• Weisstein, Eric W. "Median Triangle". MathWorld.