Step 1: Draw the triangle ABC. And recall the definition of the orthocenter.

          DEFINITION: The orthocenter is the point where the three altitudes of the triangle converge.

Step 2: Set the compasses' width to the length of a side of the triangle.

            NOTE: Any side will do, but the shortest works best.

Step 3: With the compasses on vertex B, one end of that line, draw an arc across the opposite side. Label this point with alphabet F

Step 4: Repeat for the other end of the line, by placing the compasses on vertex C. Label this point P.

            NOTE: If you find you cannot draw these arcs on the opposite sides,

                        the orthocenter is outside the triangle.

Step 4: Draw a altitude to the one side of the triangle.

          NOTE:  This is the same process as constructing a perpendicular to a line

                        through a point.

          Skill 1: With the compasses on vertex B, set the compasses' width to

                      more than half the distance to P.

        Skill 2: From B and P, draw two arcs that intersect, creating point Q.

        Skill 3: Use a straightedge to draw a line from vertex (C) to arc

                intersection point (Q). The part of this line inside the triangle forms an

                altitude of the triangle.

Step 5: In the same way construct the altitudes to the remaining sides

Step 6: Conclude that the point where the two altitudes intersect is the orthocenter of the triangle.

          NOTE: (You may need to extend the altitude lines so they intersect if the orthocenter is outside the triangle)