Given 3 line segments that are the medians of a triangle construct the original triangle.

These are given medians of a triangle.

We know that all three medians intersect at a point (M).

And where they intersect at point M is at a point two thirds of that segment, no matter what kind of triangle you have.


 

The ratios stay the same. So to construct the original triangle we tri-sect the three given segments.

Then take one of the segments (K) at a point of trisection and construct a circle using 2/3 of one of the other segments (K). Then take the remaining 1/3 of the segment (K) and construct a circle using that as the radius.


 

So I took 1/3 of segment (K) and made a point (Z).  Then from that point I took 2/3 of segment (M) from point  (Z) and the other 1/3 of segment (M) to the other side of point (Z).  Then I made a ray and had the length of segment (M).  I constructed segment (L) the same way.  The I rotated segment (J) until the rays of the lines and the points matced up to form the triangle.
So you get something that looks this. Then rotate the points until you get three endpoints that are colinear to each other. Once you match up three points the remaining point will also match up and then you have the other sides of the triangle.
 
 
 

RETURN TO RAJU'S HOME PAGE