![]() Altitudes can sometimes coincide with a side of the triangle or can sometimes meet an extended base outside the triangle. Figure 1 Three bases and three altitudes for the same triangle. The altitudes also appear in several metric relations between the elements of $\Delta ABC. Every altitude is the perpendicular segment from a vertex to its opposite side (or the extension of the opposite side) (Figure 1). An altitude of a triangle is a line which passes through a vertex of a triangle, and meets the opposite side at right angles. Using the standard notations, in $\Delta ABC$, there are three altitudes: $AH_)$ of the orthic triangle passes through the midpoints of the sides and the midpoints of the segments $AH,$ $BH,$ $CH,$ for which reason it is known as the 9-point circle. An altitude is the portion of the line between the vertex and the foot of the perpendicular. The right triangle altitude theorem or geometric mean theorem describes a relation between the lengths of the altitude on the hypotenuse in a right triangle. ![]() In a triangle, an altitude is a segment of the line through a vertex perpendicular to the opposite side. About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy
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