What term describes a line segment that connects a vertex of a triangle to a point of the line contains the opposite side so that the line segment is perpendicular to that line?

The term that describes this line segment is "altitude." In a triangle, an altitude is drawn from a vertex to the line containing the opposite side, creating a right angle with that side. Each triangle has three altitudes, one from each vertex, which can be inside or outside the triangle depending on the type of triangle.