A triangle has exactly three altitudes, one from each vertex to the opposite side. These altitudes are concurrent, meaning they intersect at a single point known as the orthocenter of the triangle. The position of the orthocenter varies depending on the type of triangle:
- In an acute triangle, all altitudes lie inside the triangle, and so does the orthocenter.
- In a right triangle, the orthocenter is located at the vertex of the right angle.
- In an obtuse triangle, the orthocenter falls outside the triangle, as two of the altitudes extend beyond the triangle’s sides.
Each altitude represents the shortest distance from a vertex to its opposite side and plays a crucial role in various geometric calculations, such as determining the area of the triangle.
