Construct any triangle ABC. Then construct the orthocenter H of triangle ABC.
Construct the orthocenter of triangle of HBC.
Construct the orthocenter of triangle HAB.
Construct the orthocenter of triangle HAC.
Any conjectures:
In this assignment, I went about constructing the orthocenters. I noticed that as I constructed the orthocenters of triangles inside the original triangle using two vertices of the original triangle and the orthocenter of the original triangle that they always lay at the vertex in the original triangle that was not being used.