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Euclid's Proposition 28 extends this result in two ways. First, if a transversal intersects two lines so that corresponding angles are congruent, then the lines are parallel. Second, if a transversal intersects two lines so that interior angles on the same side of the transversal are supplementary, then the lines are parallel.
Because parallel lines in a Euclidean plane are equidistant there is a unique distance between the two parallel lines. Given the equations of two non-vertical, non-horizontal parallel lines, = + = +, the distance between the two lines can be found by locating two points (one on each line) that lie on a common perpendicular to the parallel lines ...
Transversal. Transversals are a geometric construction on a scientific instrument to allow a graduation to be read to a finer degree of accuracy. Their use creates what is sometimes called a diagonal scale, an engineering measuring instrument which is composed of a set of parallel straight lines which are obliquely crossed by another set of straight lines.
Two lines that are parallel to the same line are also parallel to each other. In a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides (Pythagoras' theorem). [6] [7] The law of cosines, a generalization of Pythagoras' theorem. There is no upper limit to the area of a triangle. (Wallis axiom) [8]
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.
An intersection point between two arcs is transverse if and only if it is not a tangency, i.e., their tangent lines inside the tangent plane to the surface are distinct. In a three-dimensional space, two curves can be transverse only when they have empty intersection, since their tangent spaces could generate at most a two-dimensional space.
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Suppose S is the common starting point of two rays, and two parallel lines are intersecting those two rays (see figure). Let A, B be the intersections of the first ray with the two parallels, such that B is further away from S than A, and similarly C, D are the intersections of the second ray with the two parallels such that D is further away ...