Two or more lines that are parallel to the same line are not parallel to each other. Question 42Select one:TrueFalse

Break Down the Problem

1. Understand the concept of parallel lines.
2. Evaluate the relationship between the lines in question.

Relevant Concepts

Parallel lines are lines in a plane that never meet; they are always the same distance apart. If two lines are parallel to the same line, we need to determine if they must also be parallel to each other.

Analysis and Detail

1. Consider three lines: Line A, Line B, and Line C.
2. If Line A is parallel to Line B and Line A is also parallel to Line C, then by the transitive property of parallel lines, Line B and Line C must also be parallel to each other.
3. Conversely, if Line A is parallel to Line B but not to Line C, then Line B and Line C are not parallel to each other.

Verify and Summarize

The statement in question is misleading. It implies that two lines that are both parallel to a third line (but not to each other) can exist, which contradicts the definition of parallelism.

Final Answer

False. Two lines that are parallel to the same line are, in fact, parallel to each other.