Question

Read the following statement carefully and identify the true statement(a) Two lines parallel to a third line are parallel(b) Two lines perpendicular to a third line are parallel(c) Two lines parallel to a plane are parallel(d) Two lines perpendicular to a plane are parallel(e) Two lines either intersect or are parallel

A
a & b
B
a & d
C
d & e
D
a

Solution

The correct options are A a & d D a$$(a)$$ Two lines parallel to a third line are parallel-True$$(b)$$ Two lines perpendicular to a third line are parallel-False. The $$x-$$ and $$y-$$axes are both perpendicular to the $$z-$$axis, yet the $$x-$$ and $$y-$$axes are not parallel.$$(c)$$ Two lines parallel to a plane are parallel-False. The $$x-$$ and $$y-$$axes are not parallel, yet they are both parallel to the plane $$z = 1.$$$$(d)$$ Two lines perpendicular to a plane are parallel-True$$(e)$$ Two lines either intersect or are parallel-False. They can be skew.Only the statements $$(a)$$ and $$(d)$$ are true.Mathematics

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