I will begin this assignment with a triangle ABC. Then I will construct its orthocenter (H). To construct the orthocenter of ABC, I click on each point and the opposing side then make a perpendicular line.
Now I will find the orthocenter of HBC using the previous method. I will label this point H1.
The graph looks the same, why? Well since we created perpendicular lines to ABC when we use those lines as our new triangle the perpendiculars become ABC. They all meet at point A or H1.
Now I will find the orthocenter of HAB. I will label the point H2.
As you can see the point C is our orthocenter of HAB.
Now I will look at the triangle HAC and I predict that the orthocenter will be point B. Lets check the last triangle to see if our observation is correct.
From the picture one can see that the point B (or H3) was the orthocenter for HAC.