Let's start with recalling that an orthocenter of a triangle is a point of intersection of the triangle altitudes. We will draw three altitudes in a right triangle and locate its orthocenter. Let's review that an altitude of a triangle is a segment from a vertex to the line containing the opposite side and perpendicular to the line containing that side.
As we can see, since ∠ ACB is a right angle, side BC is perpendicular to AC and side AC is perpendicular to BC. Thus, these are the altitudes of △ ABC. The third altitude is CD. All the altitudes intersect at point C, which is a vertex of △ ABC.
Generally speaking, two sides of a right triangle that form a right angle are also the altitudes of a triangle and they intersect at a triangle vertex. The last altitude is going out from that vertex (as it's shown above). Therefore, the altitudes of a right triangle always intersect at its vertex. The statement is true.
