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2. Transversal (geometry) - Wikipedia

   en.wikipedia.org/wiki/Transversal_(geometry)

   In geometry, a transversal is a line that passes through two lines in the same plane at two distinct points. Transversals play a role in establishing whether two or more other lines in the Euclidean plane are parallel. The intersections of a transversal with two lines create various types of pairs of angles: consecutive interior angles ...

3. Transversal plane - Wikipedia

   en.wikipedia.org/wiki/Transversal_plane

   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.

4. Parallel (geometry) - Wikipedia

   en.wikipedia.org/wiki/Parallel_(geometry)

   In geometry, parallel lines are coplanar infinite straight lines that do not intersect at any point. Parallel planes are planes in the same three-dimensional space that never meet. Parallel curves are curves that do not touch each other or intersect and keep a fixed minimum distance.

5. Affine geometry - Wikipedia

   en.wikipedia.org/wiki/Affine_geometry

   Geometry. In mathematics, affine geometry is what remains of Euclidean geometry when ignoring (mathematicians often say "forgetting" [1][2]) the metric notions of distance and angle. As the notion of parallel lines is one of the main properties that is independent of any metric, affine geometry is often considered as the study of parallel lines.

6. Menelaus's theorem - Wikipedia

   en.wikipedia.org/wiki/Menelaus's_theorem

   Menelaus's theorem. In Euclidean geometry, Menelaus's theorem, named for Menelaus of Alexandria, is a proposition about triangles in plane geometry. Suppose we have a triangle ABC, and a transversal line that crosses BC, AC, AB at points D, E, F respectively, with D, E, F distinct from A, B, C. A weak version of the theorem states that.

7. Intercept theorem - Wikipedia

   en.wikipedia.org/wiki/Intercept_theorem

   Intercept theorem. On ratios of line segments formed when 2 intersecting lines are cut by a pair of parallels. The intercept theorem, also known as Thales's theorem, basic proportionality theorem or side splitter theorem, is an important theorem in elementary geometry about the ratios of various line segments that are created if two rays with a ...