LetŐs look at the orthocenter. The orthocenter of a triangle is the common intersection of the three lines containing the altitudes. An altitude is a perpendicular segment from a vertex to the line of the opposite side. The orthocenter does not have to be on the segments that are altitudes, but it does lie on the lines extended along the altitudes.
For acute triangles the orthocenter will be in the interior of the triangle.
For obtuse triangles the orthocenter will be outside of the triangle.
For right triangles the orthocenter will lie on the side of the triangle opposite the right angle.
Use the GSP to explore the orthocenter for yourself.