Definition:Altitude of Triangle

Definition

Let $\triangle ABC$ be a triangle.

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

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

Foot of Altitude

The point at which $h_a$ meets $BC$ (or its production) is the foot of the altitude $h_a$.

Also defined as

The word altitude is often used in the context of a geometric figure to mean the height.

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

Also see

• Definition:Cevian: of which an altitude is a specific instance

• Definition:Orthocenter

• Results about altitudes of triangles can be found here.

Sources

• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): altitude: 1.
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): altitude
• 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): altitude (geometry)