Median triangle

Median triangle: Starting triangle: Median triangle of the median triangle: Area relationship : Aspect ratio: ${\displaystyle \triangle BGF}$
${\displaystyle \triangle ABC}$
${\displaystyle \triangle BKH}$
${\displaystyle |\triangle BGF|={\tfrac {3}{4}}|\triangle ABC|}$
${\displaystyle {\tfrac {|BH|}{|BC|}}={\tfrac {|HK|}{|AB|}}={\tfrac {|BK|}{|AC|}}={\tfrac {3}{4}}}$

The median triangle or bisector triangle of a given triangle (exit triangle) is a triangle whose sides correspond to and are parallel to the bisectors of the exit triangle . The area of ​​a median triangle is the area of ​​the starting triangle . If you construct the median triangle into a median triangle, this is similar to the starting triangle of the original median triangle with a stretch factor or aspect ratio of . ${\displaystyle {\tfrac {3}{4}}}$ ${\displaystyle {\tfrac {3}{4}}}$

literature

• Roger A. Johnson: Advanced Euclidean Geometry . Dover 2007, ISBN 978-0-486-46237-0 , pp. 282-283
• Claudi Alsina, Roger B. Nelsen: Charming Proofs: A Journey Into Elegant Mathematics . MAA, 2010, ISBN 9780883853481 , p. 165
• Árpad Bényi, Branko Ćurgus: Outer Median Triangles . In: Mathematics Magazine , Volume 87, No. 3 (June 2014), pp. 185–194 ( JSTOR )

Web links

• Eric W. Weisstein : Median Triangle . In: MathWorld (English).