Difference between revisions of "Perpendicular"
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==Origin== | ==Origin== | ||
[https://nordan.daynal.org/wiki/index.php?title=English#ca._1100-1500_.09THE_MIDDLE_ENGLISH_PERIOD Middle English] ''perpendiculer'', from Middle French, from [[Latin]] ''perpendicularis'', from ''perpendiculum'' plumb line, from ''per''- + ''pendēre'' to hang | [https://nordan.daynal.org/wiki/index.php?title=English#ca._1100-1500_.09THE_MIDDLE_ENGLISH_PERIOD Middle English] ''perpendiculer'', from Middle French, from [[Latin]] ''perpendicularis'', from ''perpendiculum'' plumb line, from ''per''- + ''pendēre'' to hang | ||
| − | *[ | + | *[https://en.wikipedia.org/wiki/14th_century 14th Century] |
==Definitions== | ==Definitions== | ||
| − | *1a : standing at [ | + | *1a : standing at [https://en.wikipedia.org/wiki/Right_angle right angles] to the plane of the [[horizon]] : exactly upright |
:b : being at right angles to a given line or [[plane]] | :b : being at right angles to a given line or [[plane]] | ||
*2: extremely steep : precipitous | *2: extremely steep : precipitous | ||
| − | *3often capitalized : of or relating to a medieval [ | + | *3often capitalized : of or relating to a medieval [https://en.wikipedia.org/wiki/English_Gothic English Gothic style] of [[architecture]] in which [[vertical]] lines predominate |
*4: relating to, uniting, or consisting of [[individuals]] of dissimilar type or on [[different]] levels | *4: relating to, uniting, or consisting of [[individuals]] of dissimilar type or on [[different]] levels | ||
==Description== | ==Description== | ||
| − | In [[geometry]], the word perpendicular [[describes]] the [[relationship]] between two geometric objects that meet at a [ | + | In [[geometry]], the word perpendicular [[describes]] the [[relationship]] between two geometric objects that meet at a [https://en.wikipedia.org/wiki/Right_angle right angle]. |
| − | A [ | + | A [https://en.wikipedia.org/wiki/Line_(geometry) line] is said to be ''perpendicular'' to another line if the two lines [[intersect]] at a right angle. Explicitly, a first line is perpendicular to a second line if 1) the two lines meet and 2) at the point of intersection the straight angle on one side of the first line is cut by the second line into two [https://en.wikipedia.org/wiki/Congruence_(geometry) congruent] angles. Perpendicularity can be shown to be [[symmetric]], meaning if a first line is perpendicular to a second line, then the second line is also perpendicular to the first. For this reason, we may speak of two lines as being perpendicular (to each other) without specifying an order.[https://en.wikipedia.org/wiki/Perpendicular] |
[[Category: Mathematics]] | [[Category: Mathematics]] | ||
Latest revision as of 02:32, 13 December 2020
Origin
Middle English perpendiculer, from Middle French, from Latin perpendicularis, from perpendiculum plumb line, from per- + pendēre to hang
Definitions
- 1a : standing at right angles to the plane of the horizon : exactly upright
- b : being at right angles to a given line or plane
- 2: extremely steep : precipitous
- 3often capitalized : of or relating to a medieval English Gothic style of architecture in which vertical lines predominate
- 4: relating to, uniting, or consisting of individuals of dissimilar type or on different levels
Description
In geometry, the word perpendicular describes the relationship between two geometric objects that meet at a right angle.
A line is said to be perpendicular to another line if the two lines intersect at a right angle. Explicitly, a first line is perpendicular to a second line if 1) the two lines meet and 2) at the point of intersection the straight angle on one side of the first line is cut by the second line into two congruent angles. Perpendicularity can be shown to be symmetric, meaning if a first line is perpendicular to a second line, then the second line is also perpendicular to the first. For this reason, we may speak of two lines as being perpendicular (to each other) without specifying an order.[1]
