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Mobile App 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
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.
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