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

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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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