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what is a skew in geometry

A skew in geometry usually refers to skew lines : lines that do not intersect, are not parallel, and are not in the same plane.

Quick Scoop: Definition

  • In geometry, skew lines are:
    • Not parallel.
* Never intersecting.

* In different planes (non‑coplanar).

So, a “skew” relationship is about how two lines sit in 3D space: they miss each other forever, but not in the orderly way that parallel lines do.

Easy way to picture it

Imagine a rectangular box:

  • One edge along the top front.
  • One edge along the right side bottom.

Those two edges are:

  • Not parallel.
  • They don’t intersect.
  • They live on different faces (planes) of the box.

That pair is a classic example of skew lines.

Key facts at a glance

html

<table>
  <tr>
    <th>Type of lines</th>
    <th>Intersect?</th>
    <th>Parallel?</th>
    <th>Same plane?</th>
  </tr>
  <tr>
    <td>Intersecting</td>
    <td>Yes [web:7]</td>
    <td>No [web:7]</td>
    <td>Yes (coplanar) [web:1][web:7]</td>
  </tr>
  <tr>
    <td>Parallel</td>
    <td>No [web:7]</td>
    <td>Yes [web:7]</td>
    <td>Yes (coplanar) [web:5][web:7]</td>
  </tr>
  <tr>
    <td>Skew</td>
    <td>No [web:1][web:3]</td>
    <td>No [web:3][web:5]</td>
    <td>No (non‑coplanar, 3D only) [web:1][web:5][web:7]</td>
  </tr>
</table>

Why it only shows up in 3D

  • In a flat 2D plane, any two distinct lines are either intersecting or parallel.
  • For lines to be skew , they must lie in different planes, which needs at least three dimensions.

So when someone asks “what is a skew in geometry,” they’re almost always talking about this 3D situation with skew lines.

TL;DR: A skew in geometry (as in “skew lines”) means two lines in 3D that are in different planes, never meet, and are not parallel.

Information gathered from public forums or data available on the internet and portrayed here.