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Answer :
Final answer:
Given that line JK is parallel to line LM in the realm of mathematics, this implies that the lines are parallel, lie in the same plane, and do not intersect. Statements A, C, and D are incorrect since parallel lines can't be perpendicular or skew and they must lie in the same plane.
Explanation:
In the subject of mathematics, particularly geometry, when it is given that line JK is parallel to line LM, it means that the two lines, if extended infinitely, will never intersect or meet. This implies that the following statements are true:
- E. JK and LM are parallel. This is the definition of parallel lines. They are two lines in a plane that never meet or intersect.
- B. JK and LM lie in the same plane. Parallel lines by definition must be in the same plane. If they were in different planes, they would be called skew lines.
- F. JK and LM do not intersect. Again, the definition of parallel lines implies they will never intersect.
So, statements A, C, and D are incorrect as per the given condition.
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Rewritten by : Barada
We are given that
JK is parallel to line LM
now, we will verify each options
option-A:
we know that when two lines are parallel
they will never intersect
But two perpendicular lines always intersect
so, this is FALSE
option-B:
Two parallel lines can either lines in same plane or different plane as long they do not intersect with each other
so, this is TRUE
option-C:
Two parallel lines can either lines in same plane or different plane as long they do not intersect with each other
so, this is FALSE
option-D:
we know that
Two or more lines which have no intersections but are not parallel.
Since two lines in the plane must intersect or be parallel, skew lines can exist only in three or more dimensions
so, this is FALSE
option-E:
It is already given
so, this is TRUE
option-F:
We know that
parallel lines never intersect
so, this is TRUE
