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## Basic geometry and measurement

### Course: Basic geometry and measurement > Unit 4

Lesson 3: Parallel and perpendicular# Parallel & perpendicular lines intro

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.

## Want to join the conversation?

- What are complementary and supplementary angles?(170 votes)
- Good question!
**Complementary angles**are two angles that add up to 90°. For example, 30° + 60° = 90°, so 30° and 60° would be complementary angles.**Supplementary angles**are similar: they're two angles that add up to 180°. For example, 60° + 120° = 180°, so 60° and 120° are supplementary angles.(183 votes)

- What are skew lines? I have heard of them before, but I forgot what they are.(55 votes)
- Skew lines are lines that neither intersect nor are parallel. The idea is to realize that they lie in different coordinate planes ;)(15 votes)

- What about two lines that don't intersect where you see them, but are placed at an angle so if they continued to move in their same direction they would intersect? What kind of line/angle is that?(31 votes)
- it depends on where exactly they intersect and their slope. If 1 slope is 1/2 and another is -2 than there would be all right angles so it is perpendicular.

If it doesn't follow that 1 line has a slope that is the negative of the reciprocal of the other line's slope but they don't have the same slope than they are just considered to be intersecting lines.(28 votes)

- So meaning to say
**Perpendicular Lines**Intersect at a( 90 Degree) right angle, and**Parallel lines**never intersect.

Am i...right?(9 votes) - Why do perpendicular lines intersect? Why Can't parallel lines intersect?(6 votes)
- Parallel Lines share the same slope, but your wording is a bit incorrect. Parallel Lines
**can**intersect, if and only if the two lines have infinite intersection (So one line overlay on another).

All other lines that don't share the same slope intersects at some point (Assuming 2D) because those two lines form an angle at the intersection.(2 votes)

- When Sal Khan sir says at2:02that those lines he just drew can't be called perpendicular or parallel but they just intersect, then why can't we call them intersecting lines?
*Silly question you might think maybe , but I'm just curious!*(6 votes)- You can call them intersecting lines. Perpendicular lines are just a more specific type of intersecting lines that have special properties and because of wanting to identify these properties (for proofs or anything else) and be specific, we call those lines perpendicular lines. In some cases, like the one Sal drew at2:02, intersecting lines is the most specific you can get and there is nothing wrong with calling them that.(8 votes)

- What are lines that intersect, but aren't perpendicular called(7 votes)
- They are called the skew lines, they contain most of the lines found in the coordinate graph. Their properties are basically intersect but not at a right angle(4 votes)

- What are complementary and supplementary angles?(5 votes)
**Complementary angles**:

- two angles that add up to 90°

-*example: 10° & 80° are complementary***Supplementary angles**:

- two angles that add up to 180°

-*example: 5° & 175° are supplementary*

Hope this helps!(8 votes)

- Ok, so parallel is two lines that never cross, and perpendicular is two lines that make a right angle? and what are Complementary and Supplementary angles?(6 votes)
- 30 degrees and 60 degrees are each others complementary angles. The sum of two complementary angles is 180. 105 and 75 are each others supplementary angles. Supplementary angles are those whose angles add up to 180 degrees.(5 votes)

- cool man you know some long words ok here is my question what if 2 lines are not straight but are perpendicular? what u call them?(5 votes)
- Lines don't have to be horizontal or vertical in order to be perpendicular. Even if they're on a diagonal, as long as the slopes are the negative reciprocal of each other they are still perpendicular.(6 votes)

## 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.