Constructing the Orthocenter


The orthocenter is found by constructing three lines that are each perpendicular to each vertex point and the segment of the triangle opposite each vertex.

 The following are directions on how to find the orthocenter using GSP:

1.  Draw a triangle and label the vertices A, B, and C.

2.  Select point B and segment AC using the Select or Drag button on the left side of the screen.  Then, go to CONSTRUCT on the toolbar and select Perpendicular Line from the list.  GSP then constructs a line perpendicular to point B and segment AC.

3.  Repeat step 2 using first point A and segment CB; then using point C and segment AB.

4.  Now you can see the intersection point of the three constructed lines which is the orthocenter.  By using the Create Text and Labels button, I have labeled the intersection point as point D.