Main content

## Geometry (Eureka Math/EngageNY)

### Unit 4: Lesson 2

Topic B: Perpendicular and parallel lines in the Cartesian plane- Parallel & perpendicular lines intro
- Parallel & perpendicular lines from graph
- Parallel & perpendicular lines from graph
- Parallel lines from equation
- Parallel lines from equation (example 2)
- Parallel lines from equation (example 3)
- Perpendicular lines from equation
- Parallel & perpendicular lines from equation
- Writing equations of perpendicular lines
- Writing equations of perpendicular lines (example 2)
- Write equations of parallel & perpendicular lines
- Proof: parallel lines have the same slope
- Proof: perpendicular lines have opposite reciprocal slopes

© 2022 Khan AcademyTerms of usePrivacy PolicyCookie Notice

# Parallel & perpendicular lines intro

CCSS.Math:

Parallel lines never intersect, and perpendicular lines intersect at a 90 degree angle. Learn how to identify parallel and perpendicular lines. Created by Sal Khan.

## Video transcript

Let's think a little
bit about two terms that you'll see
throughout your geometry, and really, mathematical career. One is the idea of things
being perpendicular. And usually, people are
talking about perpendicular. Actually I'm misspelling
it-- perpendicular lines, and the idea of parallel lines. So perpendicular
lines are two lines that intersect at a right angle. So what am I talking about? So let's say that this is
one line right over here and that this is another
line right over here. We would say these two lines are
perpendicular if they intersect at a right angle. So they clearly intersect. In order for them to
intersect at a right angle, the angle formed
between these two lines needs to be 90 degrees. And if any one of these angles
is 90 degrees, the rest of them are going to be 90 degrees. So this is 90 degrees, then
these are perpendicular lines. And if that's 90
degrees, then that's going to be 90 degrees,
that's going to be 90 degrees, and that's going
to be 90 degrees. So if any of them are 90
degrees, the rest of them are 90 degrees, and we
have perpendicular lines. If you have two lines that
on a two-dimensional surface like your paper or like
the screen never intersect, they stay the same
distance apart, then we are talking
about parallel lines. So this line right over here
and this line right over here, the way I've drawn them,
are parallel lines. They aren't intersecting. They're both kind of going
in the same direction, but they're kind of shifted
versions of each other. They will never intersect
with each other. So these two are parallel. If we have two lines that,
let's say, they intersect, but they don't intersect
at a right angle, so let's say we have that
line and we have this line right over here, and they're
clearly not intersecting at a right angle, then we call
these neither perpendicular nor parallel lines. These lines just intersect.