Definition:Altitude of Triangle

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Let $\triangle ABC$ be a triangle.

Let a perpendicular be dropped from $\angle A$ to its opposite side $a$:


The line $h_a$ so constructed is called the altitude of $\angle A$.

Foot of Altitude

The point at which $h_a$ meets $BC$ is the foot of the altitude $h_a$.

Also defined as

The word altitude is often used to mean the height of a triangle.

However, on $\mathsf{Pr} \infty \mathsf{fWiki}$ it is preferred if the terms altitude and height are used specifically to mean the perpendicular and its length, to avoid confusion.

Also see

Altitudes are a type of Definition:Cevian.