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A transversal that cuts two parallel lines at right angles is called a perpendicular transversal. In this case, all 8 angles are right angles [1] When the lines are parallel, a case that is often considered, a transversal produces several congruent supplementary angles. Some of these angle pairs have specific names and are discussed below ...
The notion of transversality of a pair of submanifolds is easily extended to transversality of a submanifold and a map to the ambient manifold, or to a pair of maps to the ambient manifold, by asking whether the pushforwards of the tangent spaces along the preimage of points of intersection of the images generate the entire tangent space of the ambient manifold. [2]
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.
Transversal may refer to: Transversal (combinatorics), a set containing exactly one member of each of several other sets; Transversal (geometry), a line that intersects two or more lines at different points; Transversal (instrument making), a technique for subdividing graduations; Transversal Corporation, a software company
The corresponding angles formed by a transversal property, used by W. D. Cooley in his 1860 text, The Elements of Geometry, simplified and explained requires a proof of the fact that if one transversal meets a pair of lines in congruent corresponding angles then all transversals must do so. Again, a new axiom is needed to justify this statement.
In mathematics, geometrical transversal theory is a subfield of convex and discrete geometry that studies the intersections of classes of sets. Classical geometrical transversal theory studies the class of convex sets. Contemporary geometric transversal theory considers also more general sets, which have been studied with algebraic topology. [1]
Transversal (geometry) Triangulation; Triangulation (surveying) W. Weitzenböck's inequality This page was last edited on 7 July 2024, at 17:09 (UTC). Text is ...
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