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# If each of the two lines m and n are parallel to line p, which of the

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Math Expert
Joined: 02 Sep 2009
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If each of the two lines m and n are parallel to line p, which of the [#permalink]

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01 Aug 2017, 04:58
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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

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Re: If each of the two lines m and n are parallel to line p, which of the [#permalink]

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01 Aug 2017, 07:33
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 m and n are parallel to line p, which of the [#permalink]

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01 Aug 2017, 08:07
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 m and n are parallel to line p, which of the [#permalink]

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02 Aug 2017, 13:35
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 m and n are parallel to line p, which of the   [#permalink] 02 Aug 2017, 13:35
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