Draw an altitude from one vertex of the triangle perpendicular to the opposite side
Draw a second altitude from another vertex perpendicular to its opposite side
The point where the two altitudes intersect is the orthocenter
If needed, draw the third altitude to confirm the same intersection point
For a right triangle, the orthocenter is the right-angle vertex
For an obtuse triangle, the orthocenter lies outside the triangle
For an acute triangle, the orthocenter lies inside the triangle