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The triangle medians and the centroid.. In geometry, a median of a triangle is a line segment joining a vertex to the midpoint of the opposite side, thus bisecting that side. . Every triangle has exactly three medians, one from each vertex, and they all intersect at the triangle's cent
In geometry, a cevian is a line segment which joins a vertex of a triangle to a point on the opposite side of the triangle. [1] [2] Medians and angle bisectors are special cases of cevians.
The centroid of a triangle is the point of intersection of its medians (the lines joining each vertex with the midpoint of the opposite side). [6] The centroid divides each of the medians in the ratio 2 : 1 , {\displaystyle 2:1,} which is to say it is located 1 3 {\displaystyle {\tfrac {1}{3}}} of the distance from each side to the opposite ...
The median of a symmetric distribution which possesses a mean μ also takes the value μ. The median of a normal distribution with mean μ and variance σ 2 is μ. In fact, for a normal distribution, mean = median = mode. The median of a uniform distribution in the interval [a, b] is (a + b) / 2, which is also the mean.
Lines A, B and C are concurrent in Y. In geometry, lines in a plane or higher-dimensional space are concurrent if they intersect at a single point.. The set of all lines through a point is called a pencil, and their common intersection is called the vertex of the pencil.
The intersection point of both midlines will be the centroid of the tetrahedron. Since a tetrahedron has six edges in three opposite pairs, one obtains the following corollary: [ 8 ] In a tetrahedron, the three midlines corresponding to opposite edge midpoints are concurrent , and their intersection point is the centroid of the tetrahedron.
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In the diagram, the medians (in black) intersect at the centroid G. Because the symmedians (in red) are isogonal to the medians, the symmedians also intersect at a single point, L . This point is called the triangle's symmedian point , or alternatively the Lemoine point or Grebe point .