The Euler line and the center of mass of the triangle (centroid)
Euler line
Draw the notable points (barycenter, circumcenter and orthocenter) of the same triangle ABC. Build a straight line that passes through the orthocenter and the circumcenter.
Analysis on the Euler line
Is the barycenter in the straight line that passes through the orthocenter and the circumcenter?
Property of the Barycenter
Draw the centroid G of an triangle ABC. Then, draw the triangles ABG, BCG and ACG. Calculate the area of each of these triangles. What do you notice?
Justify the properties
Search and give references that justify the properties seen in previous exercises. paste the links here)