Altitude (geometry): Difference between revisions
Jump to navigation
Jump to search
imported>Richard Pinch (mention pedal triangle) |
imported>Richard Pinch (References: Coxeter+Greitzer) |
||
| Line 1: | Line 1: | ||
In [[triangle geometry]], an '''altitude''' is a line from a vertex perpendicular to the opposite side. It is an example of a [[Cevian line]]. The three altitudes are concurrent, meeting in the '''orthocentre'''. The feet of the three altitudes form the '''orthic triangle''' (which is thus a [[pedal triangle]]), and lie on the [[nine-point circle]]. The area of the triangle is equal to half the product of an altitude and the side it meets. | In [[triangle geometry]], an '''altitude''' is a line from a vertex perpendicular to the opposite side. It is an example of a [[Cevian line]]. The three altitudes are concurrent, meeting in the '''orthocentre'''. The feet of the three altitudes form the '''orthic triangle''' (which is thus a [[pedal triangle]]), and lie on the [[nine-point circle]]. The area of the triangle is equal to half the product of an altitude and the side it meets. | ||
==References== | |||
* {{cite book | author=H.S.M. Coxeter | coauthors=S.L. Greitzer | title=Geometry revisited | series=New Mathematical Library | volume=19 | publisher=[[MAA]] | year=1967 | isbn=0-88385-619-0 }} | |||
Revision as of 16:30, 24 November 2008
In triangle geometry, an altitude is a line from a vertex perpendicular to the opposite side. It is an example of a Cevian line. The three altitudes are concurrent, meeting in the orthocentre. The feet of the three altitudes form the orthic triangle (which is thus a pedal triangle), and lie on the nine-point circle. The area of the triangle is equal to half the product of an altitude and the side it meets.
References
- H.S.M. Coxeter; S.L. Greitzer (1967). Geometry revisited. MAA. ISBN 0-88385-619-0.