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# In the figure above, if x = y, which of the following MUST be true?

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Math Expert
Joined: 02 Sep 2009
Posts: 55670
In the figure above, if x = y, which of the following MUST be true?  [#permalink]

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25 Dec 2018, 02:12
00:00

Difficulty:

5% (low)

Question Stats:

91% (01:00) correct 9% (00:52) wrong based on 28 sessions

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In the figure above, if x = y, which of the following MUST be true?

I. ℓ2 is parallel to ℓ3
II. ℓ1 is perpendicular to ℓ2
III. Any line that intersects ℓ1 also intersects ℓ2.

A. I only
B. II only
C. III only
D. I and II only
E. I, II, and III

Attachment:

2018-12-25_1308.png [ 6.36 KiB | Viewed 282 times ]

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Intern
Joined: 17 Dec 2018
Posts: 21
Re: In the figure above, if x = y, which of the following MUST be true?  [#permalink]

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25 Dec 2018, 06:16
1
Y must be 90 degrees based on its alternate angle so X is also 90 degrees. This indicates both lines 2 and 3 run perpendicular to line 1. I believe this also means that lines 1 and 2 run parallel to each other as they must have the same slope to be perpendicular to the same line. Based on this logic III would not be true as line 3 going through 1 but never 2 is evidence to the contrary.

So IMO the answer is D.

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Re: In the figure above, if x = y, which of the following MUST be true?   [#permalink] 25 Dec 2018, 06:16
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