Answer
(a) To locate the orthocenter, it is not necessary to construct all three altitudes of a right triangle.
(b) The orthocenter of a right triangle is the vertex with the right angle.
Work Step by Step
(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.
