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# If each of the two lines L1 and L2 is parallel to line L3, which of th

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

---------------------------------------------------
Why cannot m, n, p be on the same plane? In the question it states that m & n are both // to p. C is true but why can't A be true?
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Re: If each of the two lines L1 and L2 is parallel to line L3, which of th [#permalink]
summerbummer wrote:
GMATinsight wrote:
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

---------------------------------------------------
Why cannot m, n, p be on the same plane? In the question it states that m & n are both // to p. C is true but why can't A be true?

summerbummer

Does the question ask us for answer choice that CAN be true or one that MUST be true?

All of the answer choices CAN be true...but only one (C) MUST be.
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Re: If each of the two lines L1 and L2 is parallel to line L3, which of th [#permalink]
Cant Lines m, n and p lie in the same plane ?
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Re: If each of the two lines L1 and L2 is parallel to line L3, which of th [#permalink]
A_Nishith wrote:
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 .

Cant Lines m, n and p lie in the same plane ?

­
They could. However, this is not necessarily the case, so option A is not always true.
Re: If each of the two lines L1 and L2 is parallel to line L3, which of th [#permalink]
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