Euler's Line Introduction
Construct
In the applet below,
a) Construct the perpendicular bisectors 垂直二等分線 and identify the circumcenter 外心.
b) Construct the medians 中線 and identify the centroid 重心.
c) Construct the altitudes 垂線 and identify the orthocenter 垂心.
Applet
Questions
What do you notice about the three points?
Change the shape of triangle by moving the vertices. What do you notice?
Proof
Can you prove that this line (Euler's Line) exist for any triangle? Try it. If you get stuck, look in your textbook for help.