What Are Altitudes?

A triangle's altitudes are perpendicular to a base and cross through a vertex

Altitudes are line segments that stretch from a corner (a.k.a. vertex) to the opposite side (a.k.a. base), making a right angle with the base. Altitudes are always perpendicular to their base.

If the opposite corner isn't "above" the base, the altitude goes from the vertex to an imaginary line extended from the segment that forms the triangle's base. If that sounds confusing, see the picture below for the "altitude from vertex H to base GF" in triangle FGH.

The length of an altitude from a vertex is also known as the height from that vertex. In triangle ABC below, the "height from C to AB" is the length of CD, the altitude from C to AB.

Each of they blue lines in the image above are altitudes in the triangles they're attached to. Notice that the altitude for triangle FGH, from vertex H to side GF, doesn't actually touch that triangle's base (line segment GF), but does intersect with the extension of that base.

In isosceles triangles (like triangle KLM), the altitude from the base (the side that isn't the same length as the other sides) is also that side's median. In equilateral triangles, all the altitudes are also medians.

In right triangles, the two legs (short sides) are both altitudes.