Q36 Complete each statement with the... [FREE SOLUTION]

91影视

Geometry

Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 227 pages

ISBN: 9780395977279

Chapter 3: Q36 (page 77)

Complete each statement with the word always, sometimes, or never.
Two planes parallel to the same line are parallel to each other

Short Answer

Expert verified

Two planes parallel to the same line are sometimes parallel to each other.

Step by step solution

Step 1. Relation between a non-intersecting line and a plane.

A line and a plane are parallel if they do not intersect.

Step 2. Draw the diagram

Draw the diagrams to illustrate two planes parallel to a same line and observe if the two planes are parallel to each other or not.

Step 3. State the explanation

In figure 1, two planes parallel to a same line are parallel to each other but in case 2 two planes parallel to a same line are not parallel to each other. Thus, even if the planes are parallel to the same line, those two planes can be parallel or intersect each other.

Therefore, it is clear from the explanation that two planes parallel to the same line are sometimes parallel to each other.