Intersecting Lines – Explanations & Examples

Now that you’re taking geometry or precalculus classes, you’ll be bumping into the concepts of intersecting lines multiple times. This is why we need to understand the concepts related to intersecting lines.

For now, let’s dive into a quick definition of intersecting lines:

                                   Intersecting lines are lines that meet each other at one point.

It’s amazing how a simple definition can lead us to know important properties about linear equations’ angles and systems. This article will help us understand the definition, properties, and applications of intersecting lines.

Intersecting lines definition

Intersecting lines are two or more lines that are coplanar to each other and meet at a common point.

The three pairs of lines shown above are examples of intersecting lines. See how each pair intersects at Point $\boldsymbol{O}$? We call this the point of intersection. Line segments can also intersect and have a point of intersection.

Keep in mind that three or more lines can share more than one point of intersection.

Lines $\overline{WX}$,$\overline{YZ}$, and $\overline{UV}$  intersect each other, and as can be seen, there are three points of intersection shared by the lines.

  • Lines $\overline{WX}$ and $\overline{UV}$ intersect at Point $\boldsymbol{O}$.
  • Lines $\overline{YZ}$and $\overline{UV}$ intersect at Point $\boldsymbol{N}$.
  • Lines $\overline{WX}$ and $\overline{YZ}$ intersect at Point $\boldsymbol{M}$.

The angles formed by these intersecting lines (and line segments) have interesting properties that we’ll soon learn in the next few sections.

What are some real-world examples of intersecting lines?

One way to test our understanding of intersecting lines’ definition is to think of real-world examples representing intersecting lines. Can you think of any? Here are three that can help you list down more examples:

  • Our scissors are great examples of objects that are intersecting each other and sharing a common point.
  • Crossroads also represent intersecting lines as well since they meet at intersecting points.
  • The lines of floors intersect each other as well and share points of intersection.

How do we use intersecting lines in coordinate geometry?

Want to learn what it means when two lines or curves intersect in coordinate geometry? Below are just some of the properties that we’ll learn about intersecting lines on an xy-coordinate system.

  • When two graphs of two functions intersect each other, the intersection point represents the solution when both functions are equated to each other.
  • This also means that when two lines or graphs intersection, then their equation will have a solution.
  • Lines that intersect with the $x$ and $y$-axis contain point/s of intersection, and these represent the graph’s $x$ and $y$-intercepts, respectively.

We’ll learn more about all these essentials concepts when we dive deeper into functions and solve functions by using graphs.

For now, let’s observe the properties shared by angles found at the point of intersection. In the next sections, we’ll also learn how to apply them in solving word problems that involve angles and intersecting lines.

Properties of the angles formed by intersecting lines

When two or more lines intersect, they form different angles at the point of intersection.

Lines $\overline{AB}$ and $\overline{CD}$, for example, meet at Point $\boldsymbol{O}$. They also form four angles at the point of intersection: $\angle COA$, $\angle COB$, $\angle BOD$, and $\angle AOD$.

Have you also noticed two pairs of vertical angles? If you need a refresher on what vertical angles are, you can check out this article we wrote before on vertical angles. For the case of the