Parallel Lines Definition

Parallel lines are the lines in a plane that never cross or intersect at any point, remaining constantly equidistant from one another

Parallel Lines Symbol

Parallel lines symbol is denoted as || as they never meet each other or intersect each other no matter how long they are extended. So, the symbol used to denote the parallel lines is ||. For instance, if AB is parallel to XY, we write it as AB || XY.

Parallel Lines | Definition, Properties & Formula

Parallel Lines in Maths are the lines in a plane that never cross or intersect at any point, remaining constantly equidistant from one another. These lines run alongside each other indefinitely without ever meeting, although it is sometimes said they converge at infinity. Essentially, parallel lines are lines that do not intersect.

Parallel lines are non-intersecting lines, and they meet at infinity. Broadly lines can be divided into Parallel Lines, Intersecting Lines, and Perpendicular lines.

In this article, we will learn about parallel lines, their properties, axioms, theorems, and detailed examples.

Table of Content

  • What are Parallel Lines?
  • Parallel Lines Definition
    • Parallel Lines Symbol
  • Parallel Lines Formula
  • Parallel Lines and Transversal
  • Angles in Parallel Lines
  • Properties of Parallel Lines
  • How Do You Know If Lines Are Parallel?
  • Parallel Lines Equation
  • Parallel Lines Axioms and Theorems
  • Parallel Lines are Consistent or Inconsistent
  • Parallel Lines Applications in Real-Life
  • Parallel Lines Solved Examples
  • Parallel Lines Practice Problems

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What are Parallel Lines?

Parallel lines are two or more than two lines that are always parallel to each other, and they lie on the same plane. No matter how long parallel lines are extended, they never meet. Parallel lines and intersecting lines are opposite each other. Parallel Lines are the lines that never meet or have any chance of meeting. In the diagram, parallel lines are shown in two ways, Line A is parallel to Line B, and Line X is parallel to Line Y....

Parallel Lines Definition

Parallel lines are the lines in a plane that never cross or intersect at any point, remaining constantly equidistant from one another...

Parallel Lines Formula

The slope is a measurement to determine the extent line is oriented to an axis. In general, we define slope as the tangent of the angle between the X-axis and a line. If the angle between x-axis and a given line is θ, then...

Parallel Lines and Transversal

When a line intersects two parallel lines or lines that are not parallel, it is called a transversal. Due to the transversal line, many relations among the pair of angles are created. They can be supplementary or congruent angles....

Angles in Parallel Lines

Angles are created due to transversal and parallel lines 1 and 2. Let’s take a look at the properties these angles showcase:...

Parallel Lines Properties

Below are some of the important properties of parallel lines:...

How Do You Know If Lines Are Parallel?

When two or more parallel lines are cut by a transversal, then the angle made by the transversal with the parallel lines shows some distinct properties:...

Parallel Lines Equation

In the parallel line’s equation, the slope of the lines is always the same. The equation for a straight line is in slope-intercept form, that is, y = mx + c, where m is the slope. For parallel lines, m will be the same; however, the intercept is not the same....

Parallel Lines Axioms and Theorems

Below are the axioms and theorems of parallel lines:...

Parallel Lines are Consistent or Inconsistent

In the context of systems of linear equations, if two lines are parallel, it means they have the same slope but different y-intercepts. When you solve such a system, you’ll find that there are either infinitely many solutions (if the lines coincide) or no solution (if the lines are distinct and parallel)....

Parallel Lines Applications in Real-Life

Parallel lines can easily be observed in real-life. One of the best examples of parallel lines is the railway tracks. These tracks are literally parallel lines in real life, as they are supposed to be always parallel to each other to grip the wheels of the train at all costs. Some other real-life examples of parallel lines are the edges of an almirah, scale (ruler), etc....

Summary – Parallel Lines

Parallel lines are lines on a plane that never intersect, remaining equidistant from each other indefinitely and often considered to meet only at infinity. These lines are a fundamental concept in geometry, differentiated from intersecting and perpendicular lines. Key characteristics of parallel lines include their consistent slope and the maintenance of a constant distance between them. When a transversal intersects parallel lines, it generates specific angle relationships, including equal alternate interior and exterior angles, supplementary consecutive interior angles, and equal corresponding angles....

Parallel Lines Solved Examples

Example 1: In the given figure, angle CMQ is given as 45. Find the rest of the angles....

Parallel Lines Practice Problems

Problem 1: Given the lines l1​, l2, and l3​ with slopes 5, 5, and -2 respectively, determine which lines are parallel to each other....

Parallel Lines – FAQs

What are Parallel Lines?...

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