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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
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B
a & d
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C
d & e
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D
a
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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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