### Learn math, science, English SAT & ACT from

high-quaility study
videos by expert teachers

##### Thank you for watching the video.

To unlock all 5,300 videos, start your free trial.

# Parallel and Skew Lines - Concept

###### Brian McCall

###### Brian McCall

**Univ. of Wisconsin**

J.D. Univ. of Wisconsin Law school

Brian was a geometry teacher through the Teach for America program and started the geometry program at his school

Parallel lines are two lines in the same plane that never intersect. In a coordinate plane, parallel lines can be identified as having equivalent slopes. Parallel lines are traditionally marked in diagrams using a corresponding number of chevrons. Skew lines are two lines not in the same plane that do not intersect. **Parallel and skew lines** are also important concepts in Algebra and upper-level math courses.

It's important to know about parallel lines because you're going to use it through all parts of Geometry. Technically parallel lines are two coplanar which means they share the same plane or they're in the same plane that never intersect. So if we had line l and line m, or I could say line xy and line wz, and if I told you they're parallel, first thing you're going to do is mark them. The way that you mark parallel lines is by using arrows. So some text books will use an arrow like that, other text books will draw on one more line and make arrows like that.

And you can identify parallel lines by having the same number of arrows. So if I had two arrows on this top line xy and only one arrow on wz I could not say that these are parallel. However if I drew in a second arrow here, then, from these markings I can determine that these two lines must be parallel. But how do I write that? Well, I will start by saying that my line xy so using arrows on both ends is parallel to so we use two big long marks wz. Okay? So in the drawing you mark parallel by using the arrows and when you're writing it out you're going to use these two lines that are next to each other and that look parallel.

Now, parallel lines are sometimes confused with skew lines. Skew lines are lines that are not coplanar and therefore can never intersect. So if we looked at this cube here, where we assume that we have six faces here and that their opposite faces are parallel, I can consider this face front face ab cd, and if I had some line in that face and I had some other line, so I guess I could draw an n, that line nef and if I had some other line here in this front plane, we have two lines, one in the plane of the face and one in the plane of the back face and these are never going to intersect but they're not parallel because they are not coplanar they're not in the same plane.

So on your true and false question when they say a parallel line, parallel lines are two lines that never intersect you're going to say false because you're going to say they could be skew. Parallel lines must be coplanar and they never intersect.

Please enter your name.

Are you sure you want to delete this comment?

###### Brian McCall

B.S. in Chemical Engineering, University of Wisconsin

J.D. University of Wisconsin Law School (magna cum laude)

He doesn't beat around the bush. His straightforward teaching style is effective and his subtle midwestern accent is engaging. There's never a dull moment with him.

##### Concept (1)

#### Related Topics

- Using a Protractor 24,313 views
- Angle Bisectors 21,477 views
- Supplementary and Complementary Angles 31,552 views
- Polygons 19,599 views
- Types of Triangles 26,074 views
- Perimeter 12,785 views
- Parts of a Circle 16,857 views
- Three Undefined Terms: Point, Line, and Plane 88,936 views
- Counterexample 31,501 views
- Writing a Good Definition 23,779 views
- Postulate, Axiom, Conjecture 23,226 views
- Converse 17,354 views
- Line Segments 40,105 views
- Rays 31,270 views
- Midpoints and Congruent Segments 31,263 views
- Parallel Planes and Lines 28,485 views
- Vertex and Diagonals 19,687 views
- Calculating the Midpoint 23,660 views
- Angles: Types and Labeling 28,679 views

## Comments (2)

Please Sign in or Sign up to add your comment.

## ·

Delete

## Rita · 1 year ago

Can you explain how 2 skew lines on parallel planes are possinle

## shimunov · 1 year, 7 months ago

thanks