Euler's Line

Euler's Line Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now) Sean Neo, Created with GeoGebra

Wow... this looked complicated but It seemed a little easy when I constructed it.

1. Find the 3 altitudes. We do this by creating a perpendicular line in the middle of each sides. Intersect two of the altitudes. The point where they meet is called the orthocenter.

2.Now find the 3 medians. We do this by finding the midpoint of each side and then making a line that passes through the midpoint and the point on the triangle opposite it. Again, intersect two medians and find the point where they meet. This is called the centroid.

3.Next, we find the 3 perpendicular bisectors. Select two points on each side (AB, AC, BC) then click on 'Perpendicular Bisector' to create a perpendicular bisector on the midpoint of the two sides. Once again, intersect two of the perpendicular bisectors and find the point where they meet. This is called the circumcenter.

4. Finally, use the 'Line through two points' tool and select the two outer centers.(be it the Orthocenter, Centroid or Circumcenter) The line that appears is the Euler's line!

note: Don't start with an equilateral triangle as all the lines will appear the same. To see better results, use a scalene triangle.

P.S: If you can't see the names clearly, drag the triangle around. I know, it's kind of messy. :P