What Are Intersecting Lines? - Definition & Examples

What Are Intersecting Lines? - Definition & Examples
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  • 0:05 Lines & Line Segments
  • 0:48 Intersecting Lines
  • 1:31 Multiple Lines, One Point
  • 1:50 Parallel Lines
  • 2:20 Lesson Summary
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Lesson Transcript
Instructor: Joseph Vigil
In this lesson, you'll learn the geometric definition of a line. You'll also learn what intersecting lines are and view a few examples of them. Then, you can test your knowledge in a brief quiz.

Lines & Line Segments

We know that, generally speaking, a line is a straight, 1-dimensional figure between two points. In geometry, though, there is a distinction between line segments and lines. A line segment is what you probably think of when you think of a line. It's straight and stretches between two endpoints:

a line with two endpoints

A line, however, is different from a line segment because it extends infinitely in both directions. It has no endpoints. Of course, we can't draw an infinite line, so we signify a line by placing arrowheads on both ends:

line with arrowheads at either end

We can name lines using two points they extend through. For example, we would call this line AB:

line including points a and b

We can also use a line with arrowheads above the two letters to mean the same thing:

letters A and B with arrow line above them

Intersecting Lines

Intersecting lines are two lines that share exactly one point. This shared point is called the point of intersection. Although we're dealing specifically with lines in this lesson, line segments also intersect where they share a common point. These two lines intersect at point X:

two lines meeting at point x

The point X is the one and only point at which these lines meet. In fact, if they had two points of intersection it would mean that one of these lines was curved and not actually a line. It doesn't matter at what angle lines meet. If they share a common point, they are intersecting lines. So even though these pairs of lines meet in clearly different ways, they are both sets of intersecting lines:

two sets of lines meeting at different angles

Multiple Lines, One Point

It's possible for more than two lines to share a point of intersection. For example, these three lines all intersect at point C:

three lines meeting at a point labeled c

In fact, we could put as many lines as we wanted through a common point since lines have no width. So, we can have an infinite number of lines intersecting at one point!

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