Intersecting Lines and Non-intersecting Lines: Overview, Properties

Intersecting Lines and Non-intersecting Lines: In geometry, intersecting lines are two or more lines that meet or cross in a plane. Non-intersecting lines, on the other hand, are two or more lines that never intersect. We may find several examples of intersecting lines and non-intersecting lines if we look around. Intersecting lines are formed when two or more lines meet at a common point, whereas non-intersecting lines do not meet at any point.

In this article, we will learn about intersecting and non-intersecting lines, their properties, and real-life examples. Students can get detailed information on intersecting and non-intersecting lines along with solved examples here. Continue reading to know more about intersecting lines and non-intersecting lines.

Intersecting Lines and Non-intersecting Lines: Overview

Let us review the basic concept of a line before moving on to discussing intersecting and non-intersecting lines. A line is a geometric construct made up of infinite points that stretch forever in both directions. It is narrow and straight, with no depth or width.

Small arrows at both sides of a line represent that it is extending infinitely to both sides. There are no ends to a line. If a line has an endpoint, it is referred to as a line segment.

A line may be formed from any two points that pass through them and extends in both directions. The line in the diagram above, for example, is designated by \(A B^{\leftrightarrow}\).

We will learn about two types of lines in this article:

1. Intersecting lines
2. Non-intersecting lines

Learn About Different Types of Lines in Geometry

Intersecting Lines

Intersecting lines are formed when two or more lines meet at a common point. The point of intersection is the point at which they cross each other. Examine the diagram below, which depicts two crossing lines \(a\) and \(b\), as well as the point of intersection \(O\).

Many straight lines are crossing each other and intersecting at the same point \(P\) in the figure below. These lines are called concurrent lines.

Properties of Intersecting Lines

The properties of intersecting lines are listed below to help us identify them quickly.

• Intersecting lines must meet at a single point and not at many points.
• Any angle can be used to bridge the intersecting lines. The resulting angle is always greater than \(0^\circ \) and less than \(180^\circ \).
• Two intersecting lines form a pair of vertical angles. The vertical angles have a shared vertex and are opposing angles.

In the figure given below, the vertical angles \(a\) and \(c\) are equal. In addition, \(b\) and \(d\) are equal vertical angles.

\(a+d\) equals \(180^{\circ}\) straight angle. Also, \(d+c, c+b\) and \(b+a\).

A transversal is a line in the Euclidean plane that crosses two or more lines at different locations. A transversal intersects a set of lines that may or may not be parallel. The dotted line that intersects the two lines in the picture below is referred to as a transversal.

When two intersecting lines meet at \(90^\circ \), then they are called perpendicular lines.

Intersecting Lines Example

Below we have provided the real-life uses of intersecting lines:

• Crossroads: Crossroads are formed when two roads (considered straight lines) intersect at a common point.
• Scissors: The two arms of the scissors form intersecting lines.
• Clock: Two needles passing through a common point in the clock form intersecting lines.
• English alphabet: A, T, L, M: Some English alphabets are also an example of intersecting lines.
• Edges of a Notebook: The adjacent edges of a notebook intersect each other at a right angle. Hence, it is an example of intersecting lines.

Non-Intersecting Lines

Lines that do not intersect (cut) or meet at any point are known as non-intersecting lines. Lines that do not cross are on the same plane. Non-intersecting lines, on the other hand, are lines that do not intersect at infinity. When the distance between two lines remains constant, the lines are said to be non-intersecting lines.

Non-intersecting lines are always at the same distance from one another. Parallel lines are another name for them. The sign used for “parallel to” is “\(∥\)”. Non-Intersecting lines in different directions like horizontally, vertically and diagonally are possible.

The angle between non-intersecting lines is zero. The slope of parallel lines is equal.

Examine the following diagram, which shows two non-intersecting, parallel lines ‘\(a\)’ and ‘\(b\)’ showing a perpendicular distance between them denoted by ‘\(c\)’ and ‘\(d\)’.

These lines are parallel because the lengths of the common perpendiculars at different locations on them are the same. The distance between two parallel lines is the name given to this length of equal length. In a plane, two lines will either intersect at one point or not cross at all, i.e., non-intersecting.

Properties of Non-intersecting Lines

The following points list the properties of non-intersecting lines, which help us to identify them quickly.

1. Non-intersecting lines never meet and do not share any common point. They are also known as parallel lines.
2. The distance between non-intersecting lines is always the same.
3. The length of any common perpendicular drawn between the two non-intersecting lines is always the same.

Non-intersecting Lines Examples

Below we have provided the real-life uses of non-intersecting lines:

• Rail Tracks: The distance between the railway tracks is always the same, so the tracks never meet each other. Hence they are an example of non-intersecting lines.
• Cricket Wickets: The arrangement of cricket wickets is such that they never intersect; hence, they are an example of non-intersecting lines.
• Electric Tower Wires: The wires in the electric towers are at the same distance apart; hence, they are a perfect example of non-intersecting lines.
• Running Track in a Stadium: The running track in a stadium is designed never to intersect.
• Ladder: The two sides of a ladder never intersect; hence, it is an example of non-intersecting lines.

Solved Examples on Intersecting Lines and Non-intersecting Lines

Q.1. Identify the pair of lines given below as intersecting or non-intersecting lines.

Ans: If lines are extended further in the same direction, they will probably meet at one point. As a result, the provided pair of lines is an intersecting pair.

Q.2. Give any two real-life examples of intersecting and non-intersecting lines.
Ans: Two examples of intersecting lines are given below:
Crossroads: When two straight roads meet at a common point, hence they form intersecting lines.
Scissors: A pair of scissors has two arms, and both the arms form intersecting lines.
Two examples of non-intersecting lines are listed below:
Ruler (scale): The opposite sides of a ruler are non-intersecting lines.
The rails of railway track: The rails of a railway track are parallel to each other are non-intersecting lines.

Q.3. Remembering the concept of intersecting and non-intersecting lines, answer the following questions based on the figure given below.

1) Lines \(KL\) and \(MN\) are ____ lines.
2) Are lines \(CD\) and \(AB\) perpendicular to each other?
3) Name any two pairs of non-intersecting lines.
Ans: 1) Lines \(KL\) and \(MN\) are intersecting lines, and the point of intersection is \(O\).
2) No, the lines \(CD\) and \(AB\) are not perpendicular to each other. They are non-intersecting lines.
3) \(AB || CD\) and \(EF || CD\). Hence, these are non-intersecting lines.

Q.4. Identify the types of lines?
(i)

(ii)

(iii)

Ans: (i) We can observe that three lines intersect at one point. As a result, they are concurrent lines.
(ii) We can observe how one line crosses the other two lines at different locations. As a result, line \(n\) is a transversal to the parallel lines \(l\) and \(m\).
(iii) We can see the intersection of two lines. As a result, they are intersecting lines.

Q.5. Identify the point of intersection of the lines given in the figure below:

Ans: We know that the point of intersection is the common point where the lines intersect each other. In the given figure, the points of intersection are \(M, N\) and \(O\).

Summary

In this article, we learned that intersecting lines are formed when two or more lines meet at a single location. Two intersecting lines form a pair of vertical angles. Examples of intersecting lines are crossroads, scissors, clock, edge of the notebook, etc. Non-intersecting lines are formed when the lines do not intersect (cut) or meet at any point. The angle between non-intersecting lines is zero. Furthermore, the distance between non-intersecting lines is the same. Examples of non-intersecting lines are rail tracks, cricket wickets, running tracks, ladders, etc.

Learn All About Concurrent Lines

FAQs About Intersecting Lines and Non-intersecting Lines

We have provided some frequently asked questions regarding this here:

Q.1. What do you mean by point of intersection in intersecting lines?
Ans: Intersecting lines are formed when two or more lines meet at a single location. The point of intersection is the common place where they intersect.

Q.2. What are intersecting lines that are not perpendicular?
Ans: Some lines cross each other but may not be necessarily perpendicular to each other. Such lines intersect each other at any angle which is greater than \(0^\circ \) and less than \(180^\circ \).

Q.3. What is the difference between perpendicular and intersecting lines?
Ans: When intersecting lines cross, the angle they meet is not specified. It can be any. Perpendicular lines, on the other hand, always cross at right angles \(\left({90^\circ }\right)\). All perpendicular lines intersect, but not all intersecting lines are necessarily perpendicular.

Q.4. What are intersecting lines in geometry?
Ans: Intersecting lines are formed when two or more lines in a plane cross each other. The point of intersection is the point at which they cross each other.

Q.5. What angles are formed by intersecting lines?
Ans: Intersecting lines can be crossed or intersected at any angle between \(0^\circ \) and \(180^\circ \). Perpendicular lines are formed when two intersecting lines meet at an angle of \(90^\circ \).

We hope this detailed article on the intersecting lines and non-intersecting lines helped you in your studies. If you have any doubts, queries or suggestions regarding this article, feel to ask us in the comment section and we will be more than happy to assist you.