Coplanar Lines

In other words, two or more lines are coplanar if a single plane contains them all.

Coplanar lines can be:

• Intersecting Lines
  Two lines in a plane are intersecting if they meet at a point. Mathematically, this means there is a point in space (x, y, z) that belongs to both lines.
  
• Parallel Lines
  Two or more lines in a plane are parallel if they do not intersect at any point. They have the same direction but never meet, and they lie in the same plane.
  
• Coincident Lines
  Two lines are coincident if they share all points. Since a line consists of an infinite number of points, coincident lines have all points in common. This is a special case of parallel lines. These lines are essentially the same line, even if they are represented by different equations.

The Difference Between Coplanar Lines and Skew Lines. Coplanar lines differ from skew lines because the latter are neither parallel nor intersecting. Hence, skew lines do not lie entirely on the same plane. Additionally, skew lines are a feature of three-dimensional space and cannot exist in a two-dimensional plane. In contrast, coplanar lines are a fundamental concept in Euclidean geometry.

A Practical Example

A common example of coplanar lines is lines drawn on a sheet of paper.

All lines drawn on the same sheet of paper are coplanar because they lie on the same plane, which is the surface of the paper. They can be parallel or intersecting.

Conversely, two lines drawn on two different sheets of paper placed one on top of the other (e.g., in a notebook) are not coplanar.

Andrea Minini - piva 09286581005 -
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Lines (Geometry)

• Line
• Parallel Lines
• Intersecting Lines
• Perpendicular Lines
• Oblique Lines
• Orthogonal Projections
• Distance Between Two Points
• Distance Between a Point and a Line
• Distance Between Two Lines
• Lines Cut by a Transversal
• Pencil of Lines
• Proper Pencil of Lines
  
• Pencil of Parallel Lines
• Coplanar and Skew Lines
• Vector Representation of a Line
• Equation of a Line
• Slope
• Equation of a Line Through Two Points
• Equation of a Line Through a Point with a Known Slope
• Equation of a Line Through the Origin
• Checking if Two Lines are Intersecting, Parallel, or Coincident
• Polar equation of a line

• Thales' Theorem (Thales' Correspondence)
• Theorem of Parallel Lines Pencil
• Perpendicular Line Theorem
• Theorem of Parallel Lines
• Parallel Postulate