Beyond the median
- Author:
- Jeremy Orloff
A standard result in geometry is that the medians of a triangle meet at a point and cut each other
in the ratio of 2:1
Suppose we subdivide each leg of the triangle in two parts so that the ratio of entire leg to the smaller parts is not 2:1 as in the case of medians, but rather n:1. Then we draw lines from the vertices to these points - let's call these lines n-dians.
The three n-dians no longer intersect at a point - rather they define a triangle. What is the relationship
between this triangle and the original triangle?
What can you say about the lengths of the segments determined by the intersections of the n-dians?
Can you prove {some, all} of your assertions?
Note: You can use the spreadsheet to do calculations. For example ABC is the area of triangle ABC.
Likewise GHI is the area of triangle GHI. If you want a label, put it in quotes. For example, type "ABC" into a cell.
This worksheet is a small modification of a worksheet of the same name created by Judah Schwartz: https://tube.geogebra.org/user/profile/id/25758