![median altitude geometry median altitude geometry](https://i.ytimg.com/vi/k2StuGgS8N0/maxresdefault.jpg)
CRC Concise Encyclopedia of Mathematics, Second Edition. Which of the following describes an altitude of a triangle Median and Altitude DRAFT.
![median altitude geometry median altitude geometry](http://i.stack.imgur.com/cjHWN.png)
The lengths of the medians can be obtained from Apollonius' theorem as:
![median altitude geometry median altitude geometry](https://i.ytimg.com/vi/Jy2ZEhweZVk/maxresdefault.jpg)
If the two triangles in each such pair are rotated about their common midpoint until they meet so as to share a common side, then the three new triangles formed by the union of each pair are congruent. 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. Each 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.