Triangle/Altitude/Definition

For a triangle ${\displaystyle {}A,B,C}$ in a Euclidean plane, the line running through ${\displaystyle {}A}$ and being perpendicular to the line given by ${\displaystyle {}B}$ and ${\displaystyle {}C}$, is called the altitude line through ${\displaystyle {}A}$. The line segment from ${\displaystyle {}A}$ to the line given by ${\displaystyle {}B}$ and ${\displaystyle {}C}$ is called the altitude through ${\displaystyle {}A}$.