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

Answer 1

Answer: (B), (D)

a & d
a

$\left(a\right)$ Two lines parallel to a third line are parallel-True

$\left(b\right)$ 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.

$\left(c\right)$ 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 $z=1.$

$\left(d\right)$ Two lines perpendicular to a plane are parallel-True

$\left(e\right)$ Two lines either intersect or are parallel-False. They can be skew.

Only the statements $\left(a\right)$ and $\left(d\right)$ are true.