section_path: Properties/Types
section_name: Types
paragraph_text: Types
  
  In a sense, all lines in Euclidean geometry are equal, in that, without coordinates, one can not tell them apart from one another. However, lines may play special roles with respect to other objects in the geometry and be divided into types according to that relationship. For instance, with respect to a conic (a circle, ellipse, parabola, or hyperbola), lines can be:
  
  In the context of determining parallelism in Euclidean geometry, a transversal is a line that intersects two other lines that may or not be parallel to each other.
  
  For more general algebraic curves, lines could also be:
  
  With respect to triangles we have:
  
  For a convex quadrilateral with at most two parallel sides, the Newton line is the line that connects the midpoints of the two diagonals.
  
  For a hexagon with vertices lying on a conic we have the Pascal line and, in the special case where the conic is a pair of lines, we have the Pappus line.
  
  Parallel lines are lines in the same plane that never cross. Intersecting lines share a single point in common. Coincidental lines coincide with each other—every point that is on either one of them is also on the other.
  
  Perpendicular lines are lines that intersect at right angles.
  
  In three-dimensional space, skew lines are lines that are not in the same plane and thus do not intersect each other.