Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 3: Q32 (page 77)

Complete each statement with the word always, sometimes, or never.

Two lines that are not coplanar intersect.

Short Answer

Expert verified

Two lines that are not coplanar never intersect.

Step by step solution

01

Step 1. Definition

Coplanar lines are those lines which lies in the same plane.

02

Step 2. Draw a diagram

Consider two planes such that they two lines are not coplanar and do not intersect.

03

Step 3. State the explanation

For two intersecting non-coplanar lines, take the point of intersection as A, and one other point on each line. Since, the lines intersect the three points are not colinear. Therefore, all three are in exactly in one plane. That means each line has two points in that plane, so each line is in that plane, therefore they are coplanar. But this contradicts the assumption that the lines were not coplanar. So, the assumption that non-coplanar lines intersect is wrong.

Therefore, two lines that are not coplanar never intersect.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Classify each pair of angles as alternate interior angles, same-side interior angles, corresponding angles, or none of these.

and

Use two lines of notebook paper as parallel lines and draw any

transversal. Use a protractor to measure

Measure one pair of same side interior angles. Repeat the experiment with another transversal. What appears to be true?

Complete each statement with the word always, sometimes, or never.

Two lines skew to a third line are skew to each other

Draw each figure described.

Lines d and e are skew, lines e and f are skew, and d⊥f.

State the postulate or theorem that justifies each statement.

m∠4=m∠8
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Discrete Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Decision Maths

Read Explanation

Applied Mathematics

Read Explanation

Statistics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free