The intersection of the pink lines represent the orthocenter of triangle X.
The intersection of the green lines represent the circumcenter of triangle X.
The intersection of the blue lines represent the centroid of triangle X.
Here is triangle X with each of these three set of lines and their intersections. Plot a point on each triangle center mentioned above. Carefully label the orthocenter O, the circumcenter C, and the centroid N.
What observations do you have about triangle X and its triangle centers?
These observations can be general observations or comparisons to triangle W.
Try moving the vertices of triangle X around now.
What observations do you have about the triangle centers as you move the vertices of triangle X around?