Noun
That point in which the three perpendiculars let fall from the angles of a triangle upon the opposite sides, or the sides produced, mutually intersect.
Source: Webster's dictionaryAn orthogonal line dropped from the Monge point to any face meets that face at the midpoint of the line segment between that face's orthocenter and the foot of the altitude dropped from the opposite vertex. Source: Internet
Since these intersect at the right-angled vertex, the right triangle's orthocenter —the intersection of its three altitudes—coincides with the right-angled vertex. Source: Internet
However, there is generally no orthocenter in the sense of intersecting altitudes. citation Gaspard Monge found a center that exists in every tetrahedron, now known as the Monge point: the point where the six midplanes of a tetrahedron intersect. Source: Internet
Furthermore, for any face, the twelve-point center lies at the midpoint of the corresponding Euler point and the orthocenter for that face. Source: Internet
The intersection of the altitudes is the orthocenter An altitude of a triangle is a straight line through a vertex and perpendicular to (i.e. forming a right angle with) the opposite side. Source: Internet