Transversal plane
In geometry, a transversal plane is a plane that intersects (not contains) two or more lines or planes. A transversal plane may also form dihedral angles.
01Theorems
Transversal plane theorem for lines: Lines that intersect a transversal plane are parallel if and only if their alternate interior angles formed by the points of intersection are congruent.
Transversal plane theorem for planes: Planes intersected by a transversal plane are parallel if and only if their alternate interior dihedral angles are congruent.
Transversal line containment theorem: If a transversal line is contained in any plane other than the plane containing all the lines, then the plane is a transversal plane.
Sources and credits
This article is adapted from the Wikipedia article “Transversal plane”, written by its contributors and licensed under CC BY-SA 4.0. Fathomly has changed the layout, removed citation markers, navigation and maintenance notices, and adjusted punctuation. This adapted version is shared under the same license. For references, see the original article.
Images, from Wikimedia Commons:
- Transversal planes.JPG by Gamewinner375, CC BY-SA 3.0
Fathomly is not affiliated with or endorsed by the Wikimedia Foundation. Spotted a problem? Tell us.