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# In the figure above, are l1 and l2 parallel to each other?

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Math Expert
Joined: 02 Sep 2009
Posts: 52295
In the figure above, are l1 and l2 parallel to each other?  [#permalink]

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06 Feb 2018, 04:47
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93% (00:52) correct 7% (01:24) wrong based on 23 sessions

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In the figure above, are l1 and l2 parallel to each other?

(1) x = z

(2) x + y = 180 degrees

Attachment:

2018-02-06_1645.png [ 6.77 KiB | Viewed 1550 times ]

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Re: In the figure above, are l1 and l2 parallel to each other?  [#permalink]

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06 Feb 2018, 22:26
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Bunuel wrote:

In the figure above, are l1 and l2 parallel to each other?

(1) x = z

(2) x + y = 180 degrees

Attachment:
2018-02-06_1645.png

l1 and l2 are two lines which might or might not be parallel, and both of them are being intersected by a third line l3, which is called a transversal.

(1) Angle x and Angle z are corresponding angles, if they are equal then the lines l1 and l2 have to be parallel. Because if these two angles are equal, then both lines l1 and l2 will be aligned in the plane at same inclination with respect to l3, which will make angle between l1 and l2 to be 0 degrees. This is sufficient to determine that l1 and l2 are indeed parallel.

(2) Now y + z = 180 degrees (because this is a linear pair of angles, formed on a line)
and if we are given that x + y = 180 degrees also, then we can conclude that x = z. Same as statement 1. So sufficient to determine that l1 and l2 are parallel.

Re: In the figure above, are l1 and l2 parallel to each other? &nbs [#permalink] 06 Feb 2018, 22:26
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# In the figure above, are l1 and l2 parallel to each other?

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