What do you call a line that crosses?

Intersecting lines are those lines that meet or cross each other in a plane. On the other hand, when two or more lines do not meet at any point, they are called non-intersecting lines. Let us study more about intersecting and non-intersecting lines in this article.

What are Intersecting Lines?

When two or more lines meet at a common point, they are known as intersecting lines. The point at which they cross each other is known as the point of intersection. Observe the following figure which shows two intersecting lines 'a' and 'b' and the point of intersection 'O'.

Properties of Intersecting Lines

The following points list the properties of intersecting lines which help us to identify them easily.

• Intersecting lines meet at a single point, they cannot meet at more than one point.
• Intersecting lines meet each other at any angle which is greater than 0° and less than 180°.

Non-Intersecting Lines

When two or more lines do not intersect with each other, they are termed as non-intersecting lines. Observe the following figure of two non-intersecting, parallel lines 'a' and 'b' which show a perpendicular distance denoted by 'c' and 'd'.

Properties of Non-intersecting Lines

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

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

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1. Example 1: With respect to 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.

   Solution:

1) Lines KL and MN are intersecting lines. 2) No, line CD and AB are not perpendicular to each other. They are non-intersecting, parallel lines.

3) AB || CD and EF || CD. Hence, these are non-intersecting lines.

Example 2: Identify the pair of lines given below as intersecting or non-intersecting lines.

Solution:

According to the direction of lines, if such lines are extended further, they will meet at one point. Therefore, the given pair of lines are intersecting lines.

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FAQs on Intersecting Lines

When two or more lines cross each other in a plane, they are known as intersecting lines. The point at which they cross each other is known as the point of intersection.

What is the Difference Between Perpendicular and Intersecting Lines?

When intersecting lines cross each other, there is no defined angle at which they meet, it can be any angle. However, perpendicular lines always intersect each other at right angles (90°). In other words, all perpendicular lines are intersecting lines, but all intersecting lines may not necessarily be perpendicular lines.

What are Parallel, Perpendicular, and Intersecting Lines?

Parallel lines never intersect each other and are always the same distance apart, whereas, intersecting lines cross each other and share a common point known as the point of intersection. Perpendicular lines are those intersecting lines that cross each other at an angle of 90°.

What are Intersecting Lines that are not Perpendicular?

There are some lines that intersect each other but may not be necessarily perpendicular to each other. Such lines meet at any angle which is greater than 0° and less than 180°.

What are Intersecting Lines Examples?

A few examples of intersecting lines are listed below:

• The lines of the alphabet 'X' form intersecting lines. It is a perfect example to represent intersecting lines.
• The symbol of addition (+).
• The hands of a clock.

What Angles are Formed by Intersecting Lines?

When two lines intersect each other, they form vertically opposite angles (vertical angles). Vertically opposite angles are opposite to each other and are of equal measure. Intersecting lines may cross or intersect each other at any angle greater than 0° and less than 180°. If any two intersecting lines meet each other at an angle of 90°, they are called perpendicular lines.

What are the Examples of Non-Intersecting Lines?

A few examples of non-intersecting lines are listed below:

• The opposite sides of a ruler (scale) are non-intersecting lines.
• The opposite sides of a rectangle.

What do you Mean by Point of Intersection in Intersecting Lines?

When any two lines meet at one common point, they are called intersecting lines. The common point where they intersect is known as the point of intersection.

In geometry, a  transversal  is a line that intersects two or more other (often  parallel ) lines.

In the figure below, line  n  is a transversal cutting lines  l  and  m .

When two or more lines are cut by a transversal, the angles which occupy the same relative position are called corresponding angles .

In the figure the pairs of corresponding angles are:

∠ 1  and  ∠ 5 ∠ 2  and  ∠ 6 ∠ 3  and  ∠ 7 ∠ 4  and  ∠ 8

When the lines are parallel, the corresponding angles are congruent .

When two lines are cut by a transversal, the pairs of angles on one side of the transversal and inside the two lines are called the consecutive interior angles .

In the above figure, the consecutive interior angles are:

∠ 3  and  ∠ 6 ∠ 4  and  ∠ 5

If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles formed are supplementary .

When two lines are cut by a transversal, the pairs of angles on either side of the transversal and inside the two lines are called the alternate interior angles .

In the above figure, the alternate interior angles are:

∠ 3  and  ∠ 5 ∠ 4  and  ∠ 6

If two parallel lines are cut by a transversal, then the alternate interior angles formed are congruent .

When two lines are cut by a transversal, the pairs of angles on either side of the transversal and outside the two lines are called the alternate exterior angles .

In the above figure, the alternate exterior angles are:

∠ 2  and  ∠ 8 ∠ 1  and  ∠ 7

If two parallel lines are cut by a transversal, then the alternate exterior angles formed are congruent .

Example 1:

In the above diagram, the lines j and k are cut by the transversal l . The angles ∠ c and ∠ e are…

A. Corresponding Angles

B. Consecutive Interior Angles

C. Alternate Interior Angles

D. Alternate Exterior Angles

The angles ∠ c and ∠ e lie on either side of the transversal l and inside the two lines j and k .

Therefore, they are alternate interior angles.

The correct choice is C .

Example 2:

In the above figure if lines A B ↔  and C D ↔ are parallel and m ∠ A X F = 140 °  then what is the measure of ∠ C Y E ?

The angles ∠ A X F  and ∠ C Y E  lie on one side of the transversal E F ↔ and inside the two lines A B ↔ and C D ↔ . So, they are consecutive interior angles.

Since the lines A B ↔ and C D ↔  are parallel, by the consecutive interior angles theorem ,  ∠ A X F  and ∠ C Y E  are supplementary.

That is, m ∠ A X F + m ∠ C Y E = 180 ° .

But, m ∠ A X F = 140 ° .

Substitute and solve.

140 ° + m ∠ C Y E = 180 ° 140 ° + m ∠ C Y E − 140 ° = 180 ° − 140 ° m ∠ C Y E = 40 °