Mathematics

Parallel Lines



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Points and lines are the building blocks of Euclidean plane geometry. The concept of line forms the base, for the study of angles, polygons and higher geometry.

Two lines are said to be parallel

1. Only if the lines are on the same plane.

In geometry a plane is a two dimensional surface. Two dimensional means a rectangular surface having length and breadth. Good examples of plane surfaces are blackboard, wall, a table top, or a note book page. Line is said to be one dimensional having only length as a measure.

2. Only if the lines never intersect.

Parallel lines never cross however long they are stretched in either direction. Parallel lines maintain a constant distance between them. Parallel lines do not have a common point. One can get a very good understanding of what parallel means in geometry; just by observing rails in a rail road network.

Examples of parallel lines

The opposite sides of rectangles and squares are parallel and equal. Rectangles and squares are particular case of parallelogram. Parallelograms are four sided closed figure, having opposite sides parallel and equal.

Two parallel lines have the same slope.

In algebra a line is defined by the simple equation y = mx + c where m is the slope of the line and c is the y intercept. The slope is the inclination of the line relative to the XY axis.

Concept of perpendicular lines is also of importance along with parallel lines. Two lines are said to be perpendicular if they intersect at ninety degrees. The product of slope of two mutually perpendicular lines is always -1.

Parallel lines and transversal

A transversal is a line drawn through a pair of parallel lines. It gives rise to different types of paired angles namely; corresponding angles, interior angle, exterior angles, alternate angles and vertically opposite angles. These different kinds of angles and their properties helps to find unknown angles in various geometrical figures.

Concept of parallel lines and transversal helps in deriving several geometric proofs.

In higher mathematics "Is parallel to" is an equivalence relation.A relation is said to be equivalent if it is symmetric, reflexive and transitive.

Reflexive - Line A is parallel to itself.

Symmetric - Line A is parallel to Line B implies Line B is parallel to Line A

Transitive - Line A is parallel to Line B and Line B is parallel to Line C implies Line A is parallel to Line C.

Understanding parallel lines is straightforward. The concept of parallel lines is beneficial at different stages of pure and applied mathematics.

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