温馨提示：本站仅提供公开网络链接索引服务，不存储、不篡改任何第三方内容，所有内容版权归原作者所有
AI智能索引来源：http://www.edu.com/math-glossary/Skew-Lines-Definition-Examples
点击访问原文链接

Skew Lines: Definition and Examples | EDU.COM

进入原网站 导航首页
Skew Lines: Definition and Examples | EDU.COMEDU.COMResourcesBlogGuidePodcastPlanBackHomesvg]:size-3.5">Math Glossarysvg]:size-3.5">Skew LinesSkew Lines: Definition and ExamplesTable of ContentsSkew Lines in Geometry Definition of Skew Lines

Skew lines in geometry are non-coplanar lines that are neither parallel nor intersecting. These lines can only exist in three-dimensional or higher-dimensional space, as they cannot be drawn on a flat surface. Skew lines have three key characteristics: they do not lie on the same plane (non-coplanar), they never intersect each other, and they are not parallel to one another.

Skew lines are different from both parallel lines and intersecting lines. Parallel lines lie in the same plane and never meet no matter how far they extend, while intersecting lines cross each other at a specific point and also lie in the same plane. Two lines that never cross can either be parallel (if they're in the same plane) or skew (if they're in different planes). In real life, we can see skew lines in structures like highway overpasses, on buildings where lines on different surfaces don't meet, or on 3D shapes like cubes and cuboids.

Examples of Skew Lines Example 1: Finding Shapes That Can Have Skew Lines Problem:

Which of the following shapes may have skew lines?

Rectangle Hexagons Octagon Cuboids Cube Step-by-step solution:

Step 1, Let's think about what skew lines need. Since skew lines can only exist in three-dimensional space, we need to check which shapes are 3D.

Step 2, Let's check each shape one by one. Rectangle, hexagon, and octagon are all flat shapes (2D polygons). Since they're flat, they cannot have skew lines.

Step 3, Now let's think about the cuboid and cube. Both are three-dimensional shapes with depth, width, and height. Because they are 3D shapes, they can have skew lines.

Step 4, Our answer is that only cuboids and cubes among the given options can have skew lines.

Example 2: Identifying Skew Lines on a Cube Problem:

In the figure given below, identify two pairs of skew lines on a cube.

Skew Lines

Step-by-step solution:

Step 1, Remember that skew lines must be non-intersecting, non-parallel, and non-coplanar.

Step 2, Let's look at the cube with its vertices labeled A, B, C, D at the bottom face and E, F, G, H at the top face.

Step 3, Let's check the edges AB and DH. Edge AB is on the bottom face, while DH connects the bottom and top faces. These edges don't intersect and aren't parallel. They also don't lie in the same plane. So AB and DH are skew lines.

Step 4, Now let's check edges CD and EH. Edge CD is on the bottom face, while EH is on the top face. They don't intersect, aren't parallel, and don't lie in the same plane. So CD and EH are also skew lines.

Step 5, Our two pairs of skew lines are:

AB and DH CD and EH Example 3: Drawing Skew Lines on a Cuboid Problem:

Draw a pair of skew lines in a cuboid.

Step-by-step solution:

Step 1, Let's start with a cuboid (a 3D rectangle).

Step 2, To create skew lines, we need to draw lines that don't lie in the same plane, don't intersect, and aren't parallel to each other.

Step 3, We can draw one line across the bottom face of the cuboid, going from one corner to the opposite corner.

Step 4, Then, we can draw another line across the top face, but in a different direction than the first line.

Step 5, Check that our lines are:

On different planes (one on the bottom face, one on the top face) Not parallel (they run in different directions) Not intersecting (they never meet)

Step 6, These two lines form a pair of skew lines on the cuboid.

Comments(5)SSportsTutorLanaNovember 6, 2025This skew lines def is great! It helped my students grasp the concept easily. Real-world examples made it relatable. Thanks!

CChefHenryNovember 6, 2025This glossary def of skew lines is great! It's made it so much easier for my students to understand this tricky 3D concept. Thanks!

RReaderAliceNovember 5, 2025This skew lines definition really helped my students! It made the concept clear. Would love more real-world examples though.

FFishermanFinnNovember 4, 2025This skew lines def was super helpful! I've used it to explain to my students. Real-world examples made it much easier for them to grasp.

MCMs. CarterSeptember 16, 2025I used this clear explanation of skew lines to help my kids visualize them with a cube model. It’s great to have real-world examples like highway overpasses—it really clicked for them!

Explore More TermsCircumference of The EarthEquation of A Straight LineDimeMeter to FeetLattice MultiplicationShapeView All Math TermsRecommended Interactive LessonsConvert four-digit numbers between different forms3Math3.NBT.AIdentify Patterns in the Multiplication Table3Math3.OA.D.9Use Arrays to Understand the Associative Property3Math3.OA.B.5Multiply by 53Math3.OA.C.7Find Equivalent Fractions with the Number Line3Math3.NF.A.3.a, 3.NF.A.3.bMultiply by 73Math3.OA.C.7View All Interactive LessonsRecommended VideosUse A Number Line to Add Without Regrouping1Math1.NBT.C.4Understand Arrays2Math2.OA.C.4Divide by 2, 5, and 103Math3.OA.C.7Line Symmetry4Math4.G.A.3Understand and Write Ratios6Math6.RP.A.1Powers And Exponents6Math6.EE.A.1View All VideosRecommended WorksheetsUnderstand SubtractionKMathK.OA.A.1Sort and Describe 3D Shapes1Math1.G.A.1Word Problems: Lengths2Math2.MD.B.5,2.MD.B.6Compare Decimals to The Hundredths4Math4.NF.C.7Understand Thousandths And Read And Write Decimals To Thousandths5Math5.NBT.A.3aAdd Zeros to Divide5Math5.NBT.B.7View All WorksheetsRecommended Coloring PagesElectric violin with large simple strings and no backgroundPre-K – KAll SubjectsMedlar fruit with a friendly worm popping outPre-K – KAll SubjectsPython hanging from a tree branchPre-K – KAll SubjectsSheepdog standing proudly with fluffy fur in front of a house with a picket fence2 – 3All SubjectsHorse saddle on a horse, with a detailed stable scene including hay bales and a water trough3 – 4All SubjectsA graveyard with a witch flying on a broomstick, gravestones, a tree with hanging moss, and a jack-o'-lantern5 – 6All SubjectsView All Coloring PagesRecommended BlogsWhat's a Perfect SAT Score? A Guide for K-6 FamiliesNovember 4, 2025Understanding All Five ACT Sections for K-12 Success: A Guide for Parents, Teachers, and KidsOctober 17, 2025ACT Prep Plan: Creating a Personalized Strategy for High School SuccessOctober 10, 2025ACT vs SAT: Key Differences Parents and Students Should KnowOctober 9, 2025Mastering the ACT: Smart Time Management Tips for Test SuccessOctober 9, 2025Army ASVAB Composite Scores: A Parent's Guide to Military Career PathsOctober 7, 2025View All Blog PostsQUICK LINKSAbout UsPrivacy PolicyTerms of ServiceTOOLSHomework HelperGuide DesignerPodcast MakerPlan BuilderRESOURCESMath GlossaryEnglish GlossaryEnglish Language ArtsMathematicsScienceBook InsightsFun with WordsBlog© 2025 EDU.COM. All rights reserved.

智能索引记录