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Manager  Joined: 20 Mar 2015
Posts: 54
If each of the two lines L1 and L2 is parallel to line L3, which of th  [#permalink]

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Question Stats: 83% (00:37) correct 17% (00:45) wrong based on 212 sessions

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If each of the two lines L1 and L2 is parallel to line L3, which of the following must be true?

(A) Lines L1 , L2, and L3 lie in the same plane.
(B) Lines L1 , ,L2 and L3 lie in different planes.
(C) Line L1 is parallel to line L2 .
(D) Line L1 is the same line as line L2.
(E) Line L1 is the same line as line L3 .

Manager  Joined: 19 Dec 2015
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Re: If each of the two lines L1 and L2 is parallel to line L3, which of th  [#permalink]

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If each of the two lines L1 and L2 is parallel to line L3, it means L1 || L2 || L3. And thats exactly in answer choice C.
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Re: If each of the two lines L1 and L2 is parallel to line L3, which of th  [#permalink]

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Bunuel wrote:
If each of the two lines m and n are parallel to line p, which of the following must be true?

(A) Lines m, n and p lie in the same plane
(B) Lines m, n and p are in different planes
(C) Line m is parallel to line n
(D) Line m is the same line as line n
(E) Line m is the same line as line p

The rest of the statements may or may not be true.
But, if both line m || p and n || p, line m must be definitely parallel to n(Option C)
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Re: If each of the two lines L1 and L2 is parallel to line L3, which of th  [#permalink]

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Bunuel wrote:
If each of the two lines m and n are parallel to line p, which of the following must be true?

(A) Lines m, n and p lie in the same plane
(B) Lines m, n and p are in different planes
(C) Line m is parallel to line n
(D) Line m is the same line as line n
(E) Line m is the same line as line p

(A) Lines m, n and p lie in the same plane - INCORRECT
Reasons: m and p could be in one plane and n and p could be in another plane hence not necessarily they all will be in same plane

(B) Lines m, n and p are in different planes - INCORRECT
Reasons: m, n and p could all be in one plane as well

(C) Line m is parallel to line n - CORRECT
Since m and p are parallel on one part and n and p are parallel on other plane then there must be a plane containing lines n and m as well hence they must be parallel not necessarily in the same plane containing line p as well

(D) Line m is the same line as line n - INCORRECT

(E) Line m is the same line as line p - INCORRECT

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Re: If each of the two lines L1 and L2 is parallel to line L3, which of th  [#permalink]

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Bunuel wrote:
If each of the two lines m and n are parallel to line p, which of the following must be true?

(A) Lines m, n and p lie in the same plane
(B) Lines m, n and p are in different planes
(C) Line m is parallel to line n
(D) Line m is the same line as line n
(E) Line m is the same line as line p

We have a theorem that says:

If two lines each are parallel to a third line, then they are parallel to each other.

Since line m and line n are both parallel to line p,lines m and n must also be parallel to each other.

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Intern  B
Joined: 21 Dec 2018
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Re: If each of the two lines L1 and L2 is parallel to line L3, which of th  [#permalink]

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How can we assume L1 /= L2? If L1 and L2 are the same lines then they intersect infinitely and are therefore not parallel...
Senior Manager  G
Joined: 25 Feb 2019
Posts: 335
Re: If each of the two lines L1 and L2 is parallel to line L3, which of th  [#permalink]

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t4hwg wrote:
How can we assume L1 /= L2? If L1 and L2 are the same lines then they intersect infinitely and are therefore not parallel...

There is a theoram which says

if two lines are parallel to a third line , then

all three lines are parallel to one another

means
L1 ||L3

and L2 || L3

then ,

L1 || L2 || L3

hope this helps

Posted from my mobile device
Intern  B
Joined: 21 Dec 2018
Posts: 3
Re: If each of the two lines L1 and L2 is parallel to line L3, which of th  [#permalink]

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m1033512 wrote:
t4hwg wrote:
How can we assume L1 /= L2? If L1 and L2 are the same lines then they intersect infinitely and are therefore not parallel...

There is a theoram which says

if two lines are parallel to a third line , then

all three lines are parallel to one another

means
L1 ||L3

and L2 || L3

then ,

L1 || L2 || L3

hope this helps

Posted from my mobile device

That seems rather arbitrary though doesn’t it?
For example:
L1 is (0,2) through (5,2)
L2 is Y=2
L3 is Y=0

In this case, both lines 1 and 2 are parallel to 3 but not to each other. Is there some special line nomenclature that I’m missing?
Manager  B
Joined: 16 May 2018
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Location: Hungary
Schools: Queen's MBA'20
Re: If each of the two lines L1 and L2 is parallel to line L3, which of th  [#permalink]

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1
Why is this wrong ?
(A) Lines m, n and p lie in the same plane
If they are parallel how can they be in different plane ? ( We just have x and y plane right )
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Re: If each of the two lines L1 and L2 is parallel to line L3, which of th  [#permalink]

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if L1 and L2 aren't parallel to each other then they cannot be parallel to L3 as they'd intersect at some point. Re: If each of the two lines L1 and L2 is parallel to line L3, which of th   [#permalink] 18 Jul 2019, 17:29
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