**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.**