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Pendicular lines can be parallel?
No, pendicular or can say it perpendicular lines can never be parallel as the angle b/w pendiular lines is 90 and parallel is 0 or 180 and both can not be same so ......pendicular lines cant become 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 all parallel lines have a slope of zero?
No. the slope of parallel lines would be equal but not necessarily zero. How many values can m have in " y=mx +b "? where m is the slope of the lines.
How is the Transitive Property of Parallel Lines similar to the Transitive Property of Congruence?
If A ~ B and B ~ C then A ~ C. The above statement is true is you substitute "is parallel to" for ~ or if you substitute "is congruent to" for ~.
Do lines that aren't parallel always intersect?
Yes, they do. By definition, lines that never intersect must be parallel, so all non-parallel lines must intersect at some point. Given that they are normal lines (y=mx+b) they will always have a point that suffices the equation when they are set equal to each other.
