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Intersecting Lines and Non-intersecting Lines

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Last updated date: 23rd May 2024
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Introduction

Intersecting lines are two or more lines that intersect or cross in a plane in geometry. Non-intersecting lines, on the other hand, consist of two or more lines that never intersect. If we look about, we may discover numerous examples of intersecting and non-intersecting lines. Non-intersecting lines include railway tracks and the opposing sides of a room. Intersecting lines may also be found in the corners of a room and the letter L in the English alphabet. In this article, we'll look into intersecting and non-intersecting lines, as well as their characteristics.


Before moving on to discussing intersecting and non-intersecting lines, let's examine the basic idea of a line. A line is a geometric construct made up of infinite points that stretch in both directions forever. It has no depth or width and is straight. On both sides, it is shown by little arrows. There are no boundaries to a line. A line segment is defined as a straight line with an endpoint. Any two points that pass past each other can create a line that extends in both directions. AB, for example, is the designation for the line in the diagram above.


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In this article, we'll look at two different types of lines:

  1. Intersecting lines

  2. Non-intersecting lines


Intersecting Lines Definition

When two or more lines meet at a common point, they produce intersecting lines. The point at which they cross is known as the point of intersection. Examine the diagram below, which shows two intersecting lines a and b, as well as the intersection point O.


Let's look at a couple of examples of intersecting lines.


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In the figure shown, many straight lines cross each other and intersect at the same point P. These are referred to as concurrent lines.


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Intersecting lines at various angles are as shown in the diagram above.


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An example of more than four crossing lines is shown in the diagram.

Properties of Intersecting Lines

To help us detect intersecting lines quickly, the characteristics of intersecting lines are described below.

  • Intersecting lines must intersect at a single point and not at numerous locations.

  • To connect the crossing lines, any angle can be utilised. The angle formed is always higher than 0 and less than 180 degrees.

  • A pair of vertical angles are formed by two intersecting lines. The vertical angles have the same vertex and are opposed.

  • The vertical angles a and c are equivalent in the diagram below. In addition, b and d are identical vertical angles.


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In the Euclidean plane, a transversal is a line that crosses two or more lines at distinct points. A transversal connects two or more lines that are not necessarily parallel. A transversal is a dotted line that connects the two lines in the illustration below.


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Perpendicular lines are formed when two intersecting lines meet at a 90-degree angle.


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A Real-Life Example of Intersecting Lines

  • Clock: Intersecting lines are formed by two needles passing through a common point in the clock.

  • The letters A, T, L, and M in the English alphabet are examples of intersecting lines.

  • Notebook Edges: A notebook's neighbouring edges cross at a right angle. As a result, it is an illustration of intersecting lines.

  • Crossroads: When two roads (called straight lines) intersect at a point, a crossroad is established.

  • Scissors: The scissors' two arms form intersecting lines.


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Non-Intersecting Lines

Non-intersecting lines are those that do not intersect (cut) or meet at any point. On the same plane are lines that do not cross. Lines that do not intersect at infinity are known as non-intersecting lines. Non-intersecting lines are those in which the distance between two lines remains constant. Lines that do not cross are always at the same distance apart. Another name for them is parallel lines. The symbol for "parallel to" is "||". Non-intersecting lines can be drawn in a variety of directions, including horizontally, vertically, and diagonally.


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There is no angle between non-intersecting lines. Parallel lines have the same slope.


Examine the picture below, which depicts two non-intersecting, parallel lines ‘a' and ‘b' separated by a perpendicular distance denoted by ‘c' and ‘d'.


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The lengths of the common perpendiculars at various points on these lines are the same, therefore they are parallel. This equal length is referred to by the distance between two parallel lines. Two lines in a plane will either intersect at one point or will not intersect at all, i.e., they will be non-intersecting.

Properties of Non-intersecting Lines

The characteristics of non-intersecting lines are listed below to assist us to recognise them fast.

  • Non-intersecting lines never meet and have no point in common. Another name for them is parallel lines.

  • Non-intersecting lines always have the same distance between them.

  • Any common perpendicular drawn between two non-intersecting lines will always be the same length.

Real-Life Examples of Non-Intersecting Lines

  • Rail Tracks: Since the distance between railway lines is always the same, they never cross. As a result, they are non-intersecting lines.

  • Cricket Wickets: Cricket wickets are arranged in such a way that they never intersect; hence, they are examples of non-intersecting lines.

  • Running Track at a Stadium: A stadium's running track is never built to intersect.

  • Electric tower wires are a superb example of non-intersecting lines since their wires are spaced at the same distance apart.

  • Ladder: A ladder's two sides never cross, therefore it's an example of non-intersecting lines.


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Solved Examples of Intersecting Lines and Non-Intersecting Lines

Example 1: Determine if the pair of lines below intersect or do not intersect.


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Answer:

In the above figure, both lines do not intersect with each other. But if lines are extended in the same direction any longer, they will almost certainly intersect at a certain point. As a result, the lines provided form with an intersecting pair.

Example 2: Based on the diagram below, answer the following questions about intersecting and non-intersecting lines.


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1) The lines are KL and MN is ____.

2) Are lines CD and AB parallel to each other?

3) Write the name of any two intersecting lines pairs.

4) Give the names of any two non-intersecting line pairs.


Answer:

1) The lines KL and MN intersect each other.

2) Yes lines CD and AB are parallel to each other hence, both lines do not intersect with each other.

3) The line KL and MN are intersecting line pairs and also CD and PQ lines are intersecting pairs of lines.

4) The lines EF and CD are non-intersection line pairs and also CD and AB are non-intersecting lines of pair.

A line is a geometric construct made up of infinite points that stretch in both directions. In geometry, intersecting lines are two or more lines that intersect or cross in a plane. Non-intersecting lines include railway tracks and the opposing sides of a room. This article provides a lot of real-life examples and different methods of intersecting lines and non-intersecting lines.

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FAQs on Intersecting Lines and Non-intersecting Lines

1. What are concurrent and non-concurrent lines?

If all of the lines or curves cross at the same point, they are said to be concurrent. They are non-concurrent lines if they do not cross at a single point.

2. What is the difference between intersecting lines and non-intersecting lines?

Intersecting lines are used in geometry to describe when two or more lines meet or cross in a plane. Non-intersecting lines, on the other hand, are two or more lines that do not cross at any point.

3. What are non-parallel lines called?

Two lines that do not overlap in the same three-dimensional space do not have to be parallel. Parallel lines are only called parallel if they are in the same plane; otherwise, they are called skew lines.

4. Define intersecting lines.

Intersecting lines are formed by two or more lines in a plane crossing each other. The point at which they cross is known as the point of intersection. Crossroads, Scissors and notebook edge are real-life examples of intersecting lines.