Median (Triangle)
The Cevian from a Triangle's Vertex to the Midpoint of the opposite side iscalled a median of the Triangle. The three medians of any Triangle are Concurrent, meeting in theTriangle's Centroid (which has Trilinear Coordinates 
). Inaddition, the medians of a Triangle divide one another in the ratio 2:1. A median also bisects the Area of aTriangle.
Let 
denote the length of the median of the 
th side 
. Then
 |  |  | (1) |
 | |  | (2) |
(Johnson 1929, p. 68). The Area of a Triangle can be expressed in terms of the medians by
 | (3) |
 | (4) |
A median triangle is a Triangle whose sides are equal and Parallel to the medians of a given Triangle. The median triangle of the median triangle is similar to the given Triangle in the ratio 3/4.
See also Bimedian, Exmedian, Exmedian Point, Heronian Triangle,Medial Triangle
References
Casey, J. A Sequel to the First Six Books of the Elements of Euclid, Containing an Easy Introduction to Modern Geometry with Numerous Examples, 5th ed., rev. enl. Dublin: Hodges, Figgis, & Co., 1888.
Coxeter, H. S. M. and Greitzer, S. L. Geometry Revisited. Washington, DC: Math. Assoc. Amer., pp. 7-8, 1967.
Johnson, R. A. Modern Geometry: An Elementary Treatise on the Geometry of the Triangle and the Circle. Boston, MA: Houghton Mifflin, pp. 68, 173-175, 282-283, 1929.
- Jackson's Identity
- Jackson's Theorem
- Jacobi Algorithm
- Jacobian
- Jacobian Conjecture
- Jacobian Curve
- Jacobian Determinant
- Jacobi-Anger Expansion
- Jacobian Group
- Jacobi Differential Equation
- Jacobi Differential Equation (Calculus of Variations)
- Jacobi Elliptic Functions
- Jacobi Function of the First Kind
- Jacobi Function of the Second Kind
- Jacobi-Gauss Quadrature
- Jacobi Identities
- Jacobi Matrix
- Jacobi Method
- Jacobi Polynomial
- Jacobi Quadrature
- Jacobi Rotation Matrix
- Jacobi's Curvature Theorem
- Jacobi's Determinant Identity
- Jacobi's Imaginary Transformation
- Jacobi's Theorem