Median triangle

Reference triangle: △ABC
  Median triangle: △BGF
Median triangle of △BGF: △BKH
Similarity: △BGF ~ △BKH

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:

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

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:

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

See also

• Automedian triangle

External links

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