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Medial Triangle

\begin{figure}\begin{center}\BoxedEPSF{medial_triangle.epsf scaled 700}\end{center}\end{figure}

The Triangle $\Delta M_1M_2M_3$ formed by joining the Midpoints of the sides of a Triangle $\Delta A_1A_2A_3$. The medial triangle is sometimes also called the Auxiliary Triangle (Dixon 1991). The medial triangle has Trilinear Coordinates

$\displaystyle A'$ $\textstyle =$ $\displaystyle 0:b^{-1}:c^{-1}$  
$\displaystyle B'$ $\textstyle =$ $\displaystyle a^{-1}:0:c^{-1}$  
$\displaystyle C'$ $\textstyle =$ $\displaystyle a^{-1}:b^{-1}:0.$  

The medial triangle $\Delta M_1'M_2'M_3'$ of the medial triangle $\Delta M_1M_2M_3$ of a Triangle $\Delta A_1A_2A_3$ is similar to $\Delta A_1A_2A_3$.

\begin{figure}\begin{center}\BoxedEPSF{medial_triangle2.epsf scaled 700}\end{center}\end{figure}

See also Anticomplementary Triangle


Coxeter, H. S. M. and Greitzer, S. L. Geometry Revisited. Washington, DC: Math. Assoc. Amer., pp. 18-20, 1967.

Dixon, R. Mathographics. New York: Dover, p. 56, 1991.

© 1996-9 Eric W. Weisstein