perpendicularity in Euclidean plane
Two lines in the Euclidean plane
are perpendicular
to each other if and only if they intersect and two of the angles they form are congruent.
This definition on the one in Hilbert’s Grundlagen der Geometrie (“Ein Winkel, welcher einem seiner Nebenwinkel kongruent ist, heißt ein rechter Winkel”).
The perpendicularity of and is denoted
References
- 1 D. Hilbert: Grundlagen der Geometrie. Neunte Auflage, revidiert und ergänzt von Paul Bernays. B. G. Teubner Verlagsgesellschaft, Stuttgart (1962).
| Title | perpendicularity in Euclidean plane |
| Canonical name | PerpendicularityInEuclideanPlane |
| Date of creation | 2013-04-19 15:00:12 |
| Last modified on | 2013-04-19 15:00:12 |
| Owner | pahio (2872) |
| Last modified by | pahio (2872) |
| Numerical id | 7 |
| Author | pahio (2872) |
| Entry type | Definition |
| Classification | msc 51-01 |
| Related topic | ConditionOfOrthogonality |
| Related topic | MutualPositionsOfVectors |
| Related topic | AngleBetweenTwoLines |
| Related topic | ParallellismInEuclideanPlane |
| Related topic | OrthogonalCircles |
| Related topic | DihedralAngle |
| Defines | perpendicularity |
| Defines | perpendicular |
| Defines | orthogonality |
| Defines | orthogonal |