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What is the relation between two lines perpendicular to the same line?
They're parallel.
If S equals straight lines in the plane and ab if a and b are parallel Verify that the relation is an equivalence relation on the set S given?
Establishing equivalence depends on the definition of parallel lines. If they are defined as lines which cannot ever meet (have no point in common), then the relation is not reflexive and so cannot be an equivalence relation.However, if the lines are in a coordinate plane and parallel lines are defined as those which have the same gradient then:the gradient of a is the gradient of a so the relationship is reflexive ie a ~ a.if the gradient of a is m then b is parallel to a if gradient of b = m and, if the gradient of b is m then b is parallel to a. Thus the relation ship is symmetric ie a ~ b b ~ a.If the gradient of a is m then b is parallel to a if and only if gradient of b = gradient of a, which is m. Also c is parallel to b if and only if gradient of c = gradient of b which is m. Therefore c is parallel to a. Thus the relation is transitive, that is a ~ b and b ~ c => a ~ c.The relation is reflexive, symmetric and transitive and therefore it is an equivalence relationship.
What are lines that never intersect called?
the answer is parallel lines
What are all the lines like parallel?
parallel lines are slanted lines
Can parallel lines intersect?
No, never. Parallel lines are line that will NEVER intersect.
How do lines of latitude run in relation to the equator?
Lines of latitude circle the earth, parallel to the equator.
What is the relation between two lines perpendicular to the same line?
They're parallel.
If S equals straight lines in the plane and ab if a and b are parallel Verify that the relation is an equivalence relation on the set S given?
Establishing equivalence depends on the definition of parallel lines. If they are defined as lines which cannot ever meet (have no point in common), then the relation is not reflexive and so cannot be an equivalence relation.However, if the lines are in a coordinate plane and parallel lines are defined as those which have the same gradient then:the gradient of a is the gradient of a so the relationship is reflexive ie a ~ a.if the gradient of a is m then b is parallel to a if gradient of b = m and, if the gradient of b is m then b is parallel to a. Thus the relation ship is symmetric ie a ~ b b ~ a.If the gradient of a is m then b is parallel to a if and only if gradient of b = gradient of a, which is m. Also c is parallel to b if and only if gradient of c = gradient of b which is m. Therefore c is parallel to a. Thus the relation is transitive, that is a ~ b and b ~ c => a ~ c.The relation is reflexive, symmetric and transitive and therefore it is an equivalence relationship.
Do parallel lines have the same slope?
Yes, parallel lines have the same slope. Parallel means that the lines go on forever and never cross - so, you could practically put one line on top of the other and it would have the same slope (how much it rises in relation to how far over it goes). The only difference between two lines that are parallel is their y-intercept (where they cross the y-axis).
When are two lines nonintersecting?
When two lines are parallel, then they do not intersect.
Are parallel lines actually parallel?
If they were not actually parallel then they would not be parallel lines!
Does a rectangle have parallel lines?
no parallel lines
Why does the Parthenon have no parallel lines?
it has parallel lines
What is the function of parallel lines?
parallel lines are diagonal lines or increasing lines
Does perpendicular have parallel lines?
= parallel + perpendicular As such no, perpendicular lines do not naturally have parallel lines. However...connect the lines in the symbols below. ++ ++ And you'll have 4 perpendicular lines, and 4 parallel lines.
What are lines that never intersect called?
the answer is parallel lines
Can parallel lines be intersecting lines?
No, parallel lines do not intersect, and never will.
