Median triangle

Reference triangle: Template:Math
Template:Legend-line
Median triangle of Template:Math: Template:Math
Similarity: Template:Math

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:

$$|\mathrm{△}BGF|=\frac{3}{4}|\mathrm{△}ABC|$$

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

• Template:MathWorld