the altitudes of a triangle intersect at the orthocenter.
the altitudes of a triangle intersect at the orthocenter.
where do the altitudes of a triangle intersect?
the orthocenter
the orthocenter is the intersection point of the triangle's three altitudes, each of which perpendicularly connects a side to the opposite vertex. in the case of an acute triangle, all three of these segments lie entirely in the triangle's interior, and so they intersect in the interior. but for an obtuse triangle, the altitudes from the two acute angles intersect only the extensions of the opposite sides. these altitudes









































fall entirely outside the triangle, resulting in their intersection with each other (and hence with the extended altitude from the obtuse-angled vertex) occurring in the triangle's exterior.
acute and obtuse triangles
the perpendicular bisector of a side of a triangle is the line that is perpendicular to that side and passes through its midpoint. the three perpendicular bisectors of a triangle's three sides intersect at the circumcenter (the center of the circle through the three vertices). 









































the median of a triangle's side passes through both the side's midpoint and the triangle's opposite vertex. the three medians of a triangle intersect at the triangle's centroid (the point on which the triangle would balance if it were made of a thin sheet of uniform-density metal).
midpoint