QQuestionMathematics
QuestionMathematics
"If line JK is parallel to line LM, which of the following statements are true?
A. JK and LM are perpendicular.
B. JK and LM lie in the same plane.
C. JK and LM do not lie in the same plane.
D. JK and LM are skew.
E. JK and LM are parallel.
F. JK and LM do not intersect."
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Answer
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Step 1:Let's solve this step by step:
Step 2:: Understanding Parallel Lines
When two lines are parallel, they have some specific geometric properties: - Parallel lines always maintain the same distance from each other - Parallel lines have the same slope - Parallel lines will never intersect
Step 3:: Analyzing Each Statement
A. JK and LM are perpendicular - FALSE: Parallel lines are NOT perpendicular - Perpendicular lines intersect at a 90 -degree angle - Parallel lines maintain the same angle throughout B. JK and LM lie in the same plane - TRUE: Parallel lines, by definition, must exist in the same plane - This is a fundamental property of parallel lines C. JK and LM do not lie in the same plane - FALSE: Parallel lines always exist in the same plane - If lines were not in the same plane, they would be skew lines D. JK and LM are skew - FALSE: Skew lines do not intersect and are not in the same plane - Parallel lines are always in the same plane E. JK and LM are parallel - TRUE: This is the given condition in the problem statement - Parallel lines maintain constant distance and never intersect F. JK and LM do not intersect - TRUE: Parallel lines, by definition, never intersect - They maintain the same distance and direction
Final Answer
The correct statements are B, E, and F.
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