Altitudes

An altitude of a triangle is a line segment drawn from a vertex (corner) perpendicular to the opposite side (or its extension). It represents the shortest distance from that vertex to the line containing the opposite side. Altitudes help in understanding the triangle’s height, area, and in constructing special points like the orthocenter, where all altitudes intersect. Each triangle has three altitudes, one from each vertex. They are essential in geometry for analyzing and solving problems related to angles, heights, and areas within triangles.