Euler Line (Informal Investigation)
Recall the following:
The circumcenter of a triangle is the point of concurrency (intersection) of a triangle's 3 perpendicular bisectors.
The centroid of a triangle is the point of concurrency of a triangle's 3 medians.
The orthocenter of a triangle is the point of concurrency of the lines that contain the triangle's 3 altitudes.
Check out the applet below.
Be sure to move the vertices of the black triangle around.
What do you notice?
What does this observation imply about these 3 points?
Is this observation always true even when you change the location of the triangle's 3 vertices?
See questions above applet.