Altitude (geometry): Difference between revisions
Jump to navigation
Jump to search
imported>Richard Pinch (concurrent, feet, orthic triangle) |
mNo edit summary |
||
| (5 intermediate revisions by 2 users not shown) | |||
| 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''', and lie on the [[nine-point circle]]. | {{subpages}} | ||
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 }}[[Category:Suggestion Bot Tag]] | |||
Latest revision as of 06:01, 9 July 2024
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.