## Elementary Geometry for College Students (6th Edition)

(a) To locate the orthocenter, it is not necessary to construct all three altitudes of a right triangle. (b) An altitude is a perpendicular line from a vertex of a triangle to the opposite side. The orthocenter is the point where the three altitudes of a triangle intersect. In the sketch, the altitude of vertex A is the line $AC$, and the altitude of vertex B is the line $BC$. Note that these two altitudes intersect at the point C. Also, the altitude of vertex C obviously includes the point C. Therefore, the orthocenter of any right triangle is the vertex with the right angle.