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.

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