Euler Line

Since very few students were able to determine which 3 of the 4 centers of a triangle are collinear, you are to do it again for homework. You are to draw a large scalene triangle. Construct the incenter, circumcenter, orthocenter, and centroid of the triangle. 3 of the 4 centers will lie in a straight line. Remember, draw a SCALENE triangle.

If you are havinga difficult time because of all the arcs and lines surrounding this construction, perhaps you might want to invest some money in purchasing transparencies and overhead projection markers. Then, you could draw the same triangle on 4 transparencies. On transparency #1, construct the incenter. On transparency #2, construct the circumcenter. On transparency #3, construct the orthocenter. On transparency #4, construct the centroid. Then lie all 4 transparencies on top of one another and hopefully you'll be able to determine which 3 of the 4 centers of a triangle are collinear.