![]() In 2014 Lee Sallows discovered the following theorem: The medians of any triangle dissect it into six equal area smaller triangles as in the figure above where three adjacent pairs of triangles meet at the midpoints D, E and F. (Any other lines which divide the area of the triangle into two equal parts do not pass through the centroid.) The three medians divide the triangle into six smaller triangles of equal area.Ĭonsider a triangle ABC. The centroid is twice as close along any median to the side that the median intersects as it is to the vertex it emanates from.Įach median divides the area of the triangle in half hence the name, and hence a triangular object of uniform density would balance on any median. Thus the object would balance on the intersection point of the medians. The concept of a median extends to tetrahedra.Įach median of a triangle passes through the triangle's centroid, which is the center of mass of an infinitely thin object of uniform density coinciding with the triangle. In the case of isosceles and equilateral triangles, a median bisects any angle at a vertex whose two adjacent sides are equal in length. Every triangle has exactly three medians, one from each vertex, and they all intersect each other at the triangle's 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. Not to be confused with Geometric median. ![]()
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